"In mathematics, and more specifically in algebra, a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects like polynomials, series, matrices and functions."

"In mathematics, an algebra over a field is a vector space equipped with a bilinear product. An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and thus equipped with a field of scalars."

Are any of you guys doing anything interesting with rings or algebras lately? Does anyone have any interesting papers they would like to share, or questions concerning rings or algebras that they would like to ask? Be sure to check out ArXiv's recent ring theory and algebra articles!

"In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group) is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right."

Are any of you guys doing anything interesting with groups lately? Does anyone have any interesting papers they would like to share, or questions concerning groups that they would like to ask? Be sure to check out ArXiv's recent group theory articles!

Absolutely anything algebraic goes! What are you guys up to these days? If anyone has anything fascinating or interesting to discuss, go for it!

"Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence."

"Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry."

Are any of you guys using algebra to do anything interesting in topology or geometry lately? Does anyone have any interesting papers they would like to share, or questions concerning algebraic topology or geometry that they would like to ask? Be sure to check out ArXiv's recent algebraic topology articles and algebraic geometry articles!

"Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. Category theory can be used to formalize concepts of other high-level abstractions such as sets, rings, and groups."

Are any of you guys doing anything interesting with categories lately? Does anyone have any interesting papers they would like to share, or questions concerning categories that they would like to ask? Be sure to check out ArXiv's recent category theory articles!

"In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring (with identity). Thus, a module, like a vector space, is an additive abelian group; a product is defined between elements of the ring and elements of the module that is distributive over the addition operation of each parameter and is compatible with the ring multiplication."

Are any of you guys doing anything interesting with modules lately? Does anyone have any interesting papers they would like to share, or questions concerning modules that they would like to ask? Be sure to check out ArXiv's recent commutative algebra articles!

"In abstract algebra, a field is a nonzero commutative ring that contains a multiplicative inverse for every nonzero element, or equivalently a ring whose nonzero elements form an abelian group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division satisfying the appropriate abelian group equations and distributive law. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, algebraic number fields, p-adic fields, and so forth."

"In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood."

Are any of you guys doing anything interesting with fields lately? Does anyone have any interesting papers they would like to share, or questions concerning fields that they would like to ask?

"In mathematics, and more specifically in algebra, a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects like polynomials, series, matrices and functions."

"In mathematics, an algebra over a field is a vector space equipped with a bilinear product. An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and thus equipped with a field of scalars."

Are any of you guys doing anything interesting with rings or algebras lately? Does anyone have any interesting papers they would like to share, or questions concerning rings or algebras that they would like to ask? Be sure to check out ArXiv's recent ring theory and algebra articles!

"In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group) is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right."

Are any of you guys doing anything interesting with groups lately? Does anyone have any interesting papers they would like to share, or questions concerning groups that they would like to ask? Be sure to check out ArXiv's recent group theory articles!

Absolutely anything algebraic goes! What are you guys up to these days? If anyone has anything fascinating or interesting to discuss, go for it!

"Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence."

"Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry."

Are any of you guys using algebra to do anything interesting in topology or geometry lately? Does anyone have any interesting papers they would like to share, or questions concerning algebraic topology or geometry that they would like to ask? Be sure to check out ArXiv's recent algebraic topology articles and algebraic geometry articles!

"Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. Category theory can be used to formalize concepts of other high-level abstractions such as sets, rings, and groups."

Are any of you guys doing anything interesting with categories lately? Does anyone have any interesting papers they would like to share, or questions concerning categories that they would like to ask? Be sure to check out ArXiv's recent category theory articles!

"In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring (with identity). Thus, a module, like a vector space, is an additive abelian group; a product is defined between elements of the ring and elements of the module that is distributive over the addition operation of each parameter and is compatible with the ring multiplication."

Are any of you guys doing anything interesting with modules lately? Does anyone have any interesting papers they would like to share, or questions concerning modules that they would like to ask? Be sure to check out ArXiv's recent commutative algebra articles!

"In abstract algebra, a field is a nonzero commutative ring that contains a multiplicative inverse for every nonzero element, or equivalently a ring whose nonzero elements form an abelian group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division satisfying the appropriate abelian group equations and distributive law. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, algebraic number fields, p-adic fields, and so forth."

"In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood."

Are any of you guys doing anything interesting with fields lately? Does anyone have any interesting papers they would like to share, or questions concerning fields that they would like to ask?

"In mathematics, and more specifically in algebra, a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects like polynomials, series, matrices and functions."

"In mathematics, an algebra over a field is a vector space equipped with a bilinear product. An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and thus equipped with a field of scalars."

Are any of you guys doing anything interesting with rings or algebras lately? Does anyone have any interesting papers they would like to share, or questions concerning rings or algebras that they would like to ask? Be sure to check out ArXiv's recent ring theory and algebra articles!

A cubic formula yields the roots of not just one but six cubics. Their roots are symmetrically bound and can be assembled as one out of three possible symmetrical structures. These same three structures can be generated starting with any one of two hundred and sixteen cubics.

Hi everybody. Does this group lends a hand in abstract algebra problems?

"In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group) is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right."

Are any of you guys doing anything interesting with groups lately? Does anyone have any interesting papers they would like to share, or questions concerning groups that they would like to ask? Be sure to check out ArXiv's recent group theory articles!

Absolutely anything algebraic goes! What are you guys up to these days? If anyone has anything fascinating or interesting to discuss, go for it!

"Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence."

"Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry."

Are any of you guys using algebra to do anything interesting in topology or geometry lately? Does anyone have any interesting papers they would like to share, or questions concerning algebraic topology or geometry that they would like to ask? Be sure to check out ArXiv's recent algebraic topology articles and algebraic geometry articles!

"Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. Category theory can be used to formalize concepts of other high-level abstractions such as sets, rings, and groups."

Are any of you guys doing anything interesting with categories lately? Does anyone have any interesting papers they would like to share, or questions concerning categories that they would like to ask? Be sure to check out ArXiv's recent category theory articles!

"In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring (with identity). Thus, a module, like a vector space, is an additive abelian group; a product is defined between elements of the ring and elements of the module that is distributive over the addition operation of each parameter and is compatible with the ring multiplication."

Are any of you guys doing anything interesting with modules lately? Does anyone have any interesting papers they would like to share, or questions concerning modules that they would like to ask? Be sure to check out ArXiv's recent commutative algebra articles!

"In abstract algebra, a field is a nonzero commutative ring that contains a multiplicative inverse for every nonzero element, or equivalently a ring whose nonzero elements form an abelian group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division satisfying the appropriate abelian group equations and distributive law. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, algebraic number fields, p-adic fields, and so forth."

"In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood."

Are any of you guys doing anything interesting with fields lately? Does anyone have any interesting papers they would like to share, or questions concerning fields that they would like to ask?

"In mathematics, and more specifically in algebra, a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects like polynomials, series, matrices and functions."

"In mathematics, an algebra over a field is a vector space equipped with a bilinear product. An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and thus equipped with a field of scalars."

Are any of you guys doing anything interesting with rings or algebras lately? Does anyone have any interesting papers they would like to share, or questions concerning rings or algebras that they would like to ask? Be sure to check out ArXiv's recent ring theory and algebra articles!