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

Published online by Cambridge University Press:  20 November 2018

Vesselin Drensky
Affiliation:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev Str., Block 8, 1113 Sofia Bulgaria, e-mail: [email protected]
Lakhdar Hammoudi
Affiliation:
Department of Mathematics Ohio University 101 University Drive Chillicothe, OH 45601 U.S.A, e-mail: [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

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