On monomial algebras
Let X be a finitely generated free semigroup and let I be an ideal of X. The structure and properties of the contracted semigroup ring K[X/I] of the Rees factor semigroup X/I over a field K are investigated. Among other things, the Jacobson radical and the chain conditions for K[X/I] are discussed. The main result shows that K[X/I] is a PI-algebra if and only if X/I satisfies a permutational property, that is there exists \(n\geq 2\) such that for any \(a_ 1,...,a_ n\in X/I\) there is a nontrivial permutation \(\sigma\) with \(a_ 1...a_ n=a_{\sigma (1)}...a_{\sigma (n)}\).
scientific article; zbMATH DE number 4019343
scientific article