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

  Published:2004-09-01
 Printed: Sep 2004
  • Vesselin Drensky
  • Lakhdar Hammoudi
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Abstract

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 transparent than in the past the close relationship between the considered problem and combinatorics of words.
Keywords: locally nilpotent rings, nil rings, locally nilpotent semigroups, semigroup algebras, monomial algebras, infinite words locally nilpotent rings, nil rings, locally nilpotent semigroups, semigroup algebras, monomial algebras, infinite words
MSC Classifications: 16N40, 16S15, 20M05, 20M25, 68R15 show english descriptions Nil and nilpotent radicals, sets, ideals, rings
Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]
Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
Combinatorics on 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
 

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