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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  and
Lakhdar Hammoudi
Vesselin Drensky
Affiliation:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev Str., Block 8, 1113 Sofia Bulgaria, e-mail: drensky@math.bas.bg
Lakhdar Hammoudi
Affiliation:
Department of Mathematics Ohio University 101 University Drive Chillicothe, OH 45601 U.S.A, e-mail: hammoudi@ohio.edu
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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.

Keywords

16N4016S1520M0520M2568R15locally nilpotent ringsnil ringslocally nilpotent semigroupssemigroup algebrasmonomial algebrasinfinite words
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 343 - 353
Copyright
Copyright © Canadian Mathematical Society 2004

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