Geodesic
Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras
Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 343-353

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DOI

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.
DOI : 10.4153/CMB-2004-033-2
Mots-clés : 16N40, 16S15, 20M05, 20M25, 68R15, locally nilpotent rings, nil rings, locally nilpotent semigroups, semigroup algebras, monomial algebras, infinite words 
Drensky, Vesselin; Hammoudi, Lakhdar. Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras. Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 343-353. doi: 10.4153/CMB-2004-033-2
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     author = {Drensky, Vesselin and Hammoudi, Lakhdar},
     title = {Combinatorics of {Words} and {Semigroup} {Algebras} {Which} {Are} {Sums} of {Locally} {Nilpotent} {Subalgebras}},
     journal = {Canadian mathematical bulletin},
     pages = {343--353},
     year = {2004},
     volume = {47},
     number = {3},
     doi = {10.4153/CMB-2004-033-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-033-2/}
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