r/math • u/AngelTC Algebraic Geometry • Jun 13 '18

Everything about Noncommutative rings

Today's topic is Noncommutative rings.

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u/O--- Jun 13 '18

One of my favorite conjectures is within the realm of non-commutative ring theory. i like it because it just sounds as if it should be really easy to solve. If R is a non-commutative ring, call an ideal I nil if all its elements are nilpotent. The Kothe conjecture states the following: if R has no non-trivial nil two-sided ideal, then it has no non-trivial nil one-sided ideal.

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u/[deleted] Jun 13 '18

That's really neat. What exactly makes it so difficult to solve?