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 o...

We exhibit the elementary but somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals. It leads to the construction of a bountiful set of Cohen–Macaulay Rees algebras.

The purpose of this paper is to introduce the concept graded 2-prime ideals as a new generalization prime ideals. We show that and semi-prime are different. Furthermore, we weakly also Several properties investigated. study rings in which every ideal prime, call such ring 2-P-ring. Moreover, semi-primary ideals, different concepts. In fact, semi-primary, primary equivalent over Z-graded princip...

The notions of prime(semiprime) fuzzy h-ideal(h-biideal, h-quasi-ideal) in Γ-hemiring are introduced and some of their characterizations are obtained by using ”belongingness(∈)” and ”quasi − coincidence(q)”. Cartesian product of prime(semiprime) fuzzy h-ideals of Γ-hemirings are also investigated. Keywords—Γ-hemiring, Fuzzy h-ideals, Prime fuzzy left h-ideal, Prime(semiprime) (∈,∈ ∨q)-fuzzy lef...

in a commutative noetherian local complex normed algebra which is complete in its m-adic metric there are only finitely many closed prime ideals.

A complete determination of the prime ideals invariant under winding automorphisms in the generic 3 × 3 quantum matrix algebra Oq(M3(k)) is obtained. Explicit generating sets consisting of quantum minors are given for all of these primes, thus verifying a general conjecture in the 3 × 3 case. The result relies heavily on certain tensor product decompositions for winding-invariant prime ideals, ...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...