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Search: MSC category 16S15 ( Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) )

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1. CMB 2016 (vol 59 pp. 461)

Ara, Pere; O'Meara, Kevin C.
The Nilpotent Regular Element Problem
We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element $x$ need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent element $x$ are regular.

Keywords:nilpotent element, von Neumann regular element, unit-regular, Bergman's normal form
Categories:16E50, 16U99, 16S10, 16S15

2. CMB 2004 (vol 47 pp. 343)

Drensky, Vesselin; Hammoudi, Lakhdar
Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras
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
Categories:16N40, 16S15, 20M05, 20M25, 68R15

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