In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...

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...

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

‎‎in this paper‎, ‎we define fuzzy subnexuses over a nexus $n$‎. ‎define and study the notions of the prime fuzzy subnexuses and the fractions‎‎induced by them‎. ‎finally‎, ‎we show that if s is a meet‎‎closed subset of the set fsub(n), ‎of fuzzy subnexuses of a nexus n‎, ‎and‎‎h= ⋀s ϵ s, ‎then the fractions s^-1 n and h^-1 n are isomorphic as meet-semilattices‎.

$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...