2009/04/10 by Qiaser Mushtaq, Madad Khan, Mushtaq, Qiaser +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.0904.1635
6 pages, 1table
arxiv created 2009/04/10 · openalex publication_date 2009/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.