Ideals in Left Almost Semigroups
| dc.creator | Mushtaq, Qiaser | |
| dc.creator | Khan, Madad | |
| dc.date | 2009-04-10 | |
| dc.date.accessioned | 2026-07-07T13:02:24Z | |
| dc.date.available | 2026-07-07T13:02:24Z | |
| dc.description | A left almost semigroup (LA-semigroup) or an Abel-Grassmann's groupoid (AG-groupoid) is investigated in several papers. In this paper we have discussed ideals in LA-semigroups. Specifically, we have shown that every ideal in an LA-semigroup S with left identity e is prime if and only if it is idempotent and the set of ideals of S is totally ordered under inclusion. We have shown that an ideal of S is prime if and only if it is semiprime and strongly irreducible. We have proved also that every ideal in a regular LA-semigroup S is prime if and only if the set of ideals of S is totally ordered under inclusion. We have proved in the end that every ideal in S is prime if and only if it is strongly irreducible and the set of ideals of S form a semilattice. | |
| dc.description | 6 pages, 1table | |
| dc.identifier | https://arxiv.org/abs/0904.1635 | |
| dc.identifier | http://arxiv.org/abs/0904.1635 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226436 | |
| dc.subject | Group Theory | |
| dc.title | Ideals in Left Almost Semigroups | |
| dc.type | text |