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Results tagged with ra.rings-and-algebras
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user 146681
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.
3
votes
What is an example of a Frobenius algebra that is not Koszul?
Probably the simplest example is $k[x|x^3=0]$. It is not Koszul since it is not quadratic.
7
votes
Are there three non-commutative polynomials in three variables with finite dimensional quoti...
Q1. Yes, such 3 monomials exist. Moreover, the generic homogeneous quadratic polynomials $f,g,h$ are such that the dimension of the quotient algebra $K⟨x,y,z⟩/(f,g,h)$ is 28. This follows, in particul …