Canad. Math. Bull. 47(2004), 343-353
Printed: Sep 2004
We construct new examples of non-nil algebras with any number of
generators, which are direct sums of two
locally nilpotent subalgebras. Like all previously known examples, our examples
are contracted semigroup algebras and the underlying semigroups are unions
of locally nilpotent subsemigroups.
In our constructions we make more
than in the past the close relationship between the considered problem
and combinatorics of words.
locally nilpotent rings, nil rings, locally nilpotent semigroups, semigroup algebras, monomial algebras, infinite words
16N40 - Nil and nilpotent radicals, sets, ideals, rings
16S15 - Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
20M05 - Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]
20M25 - Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
68R15 - Combinatorics on words