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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

10 votes

Examples of Non-Power Associative Algebras

The algebras known variously as left-symmetric algebras (or right-symmetric algebras), Vinberg algebras, or pre-Lie algebras are in general not power associative. These algebras occur in at least two …
Dan Fox's user avatar
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47 votes
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Have you ever seen this bizarre commutative algebra?

This algebra is defined on the permutation module of the symmetric group. It was studied by K. Harada and R. Griess in the 1970s and a proof that its automorphism group is the symmetric group can als …
Dan Fox's user avatar
  • 2,139