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ALGEBRAS WITH COLLAPSING MONOMIALS

Published online by Cambridge University Press:  01 September 1998

DAVID MICHAEL RILEY
DAVID MICHAEL RILEY
Affiliation:
Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487-0350, USA
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Abstract

A semigroup S is called collapsing if there exists a positive integer n such that for every subset of n elements in S, at least two distinct words of length n on these letters are equal in S. In particular, S is collapsing whenever it satisfies a law. Let [Uscr ](A) denote the group of units of a unitary associative algebra A over a field k of characteristic zero. If A is generated by its nilpotent elements, then the following conditions are equivalent: [Uscr ](A) is collapsing; [Uscr ](A) satisfies some semigroup law; [Uscr ](A) satisfies the Engel condition; [Uscr ](A) is nilpotent; A is nilpotent when considered as a Lie algebra.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 5 , September 1998 , pp. 521 - 528
Copyright
© The London Mathematical Society 1998

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