Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras

[摘要] We construct new examples of non-nil algebras with any number ofgenerators, which are direct sums of twolocally nilpotent subalgebras. Like all previously known examples, our examplesare contracted semigroup algebras and the underlying semigroups are unionsof locally nilpotent subsemigroups. In our constructions we make moretransparentthan in the past the close relationship between the considered problemand combinatorics of words.

[学科分类] 数学（综合）

[关键词] locally nilpotent rings;nil rings;locally nilpotent semigroups;semigroup algebras;monomial algebras;infinite words