Ideals in Left Almost Semigroups

Details Ideals in Left Almost Semigroups Ideals in Left Almost Semigroups

2009-04-10

arxiv.org/abs/0904.1635v1

Mathematics

Group Theory

6 pages, 1table

Scientific paper

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.

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