Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T15:58:07.888Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)