Associative algebras satisfying a semigroup identity
| dc.creator | Riley, David M. | |
| dc.creator | Wilson, Mark C. | |
| dc.date | 1998-02-06 | |
| dc.date.accessioned | 2026-07-07T05:23:48Z | |
| dc.date.available | 2026-07-07T05:23:48Z | |
| dc.description | Denote by (R,.) the multiplicative semigroup of an associative algebra R over an infinite field, and let (R,*) represent R when viewed as a semigroup via the circle operation x*y=x+y+xy. In this paper we characterize the existence of an identity in these semigroups in terms of the Lie structure of R. Namely, we prove that the following conditions on R are equivalent: the semigroup (R,*) satisfies an identity; the semigroup (R,.) satisfies a reduced identity; and, the associated Lie algebra of R satisfies the Engel condition. When R is finitely generated these conditions are each equivalent to R being upper Lie nilpotent. | |
| dc.description | 11 pages; written in LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/9802039 | |
| dc.identifier | http://arxiv.org/abs/math/9802039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76585 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16R40 (Primary) 20M07, 20M25 (Secondary) | |
| dc.title | Associative algebras satisfying a semigroup identity | |
| dc.type | text |