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- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S0024609398004597
- Publisher site
- See Article on Publisher Site
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 U(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: U(A) is collapsing; U(A) satisfies some semigroup law; U(A) satisfies the Engel condition; U(A) is nilpotent; A is nilpotent when considered as a Lie algebra.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Sep 1, 1998