Abstract
In this paper, we define the concept of direct product of finite fuzzy normal subrings over nonassociative and non-commutative rings (LA-ring) and investigate the some fundamental properties of direct product of fuzzy normal subrings.
Highlights
In 1972, a generalization of commutative semigroups has been established by Kazim et al [12]
We define the concept of direct product of finite fuzzy normal subrings over nonassociative and non-commutative rings (LA-ring) and investigate the some fundamental properties of direct product of fuzzy normal subrings
Let a ∈ S, Sa is a left ideal of S containing a by the Lemma 3.5.This implies that Sa is a quasi-ideal of S, so χSa is a fuzzy quasi-ideal of S by the Theorem 2.4
Summary
In 1972, a generalization of commutative semigroups has been established by Kazim et al [12]. In ternary commutative law: abc = cba, they introduced the braces on the left side of this law and explored a new pseudo associative law, that is (ab)c = (cb)a This law (ab)c = (cb)a is called the left invertive law. Fuzzy left (right, interior, quasi-, bi-, generalized bi-) ideals; regular (intra-regular) ordered AG-. In [14, 15], an ordered semigroup S is said to be an intra-regular if for every a ∈ S there exist elements x, y ∈ S such that a ≤ xa2y. Right, interior, quasi-, bi-, generalized bi-) ideals of an ordered AG-groupoid S. Intra-regular, both regular and intra-regular) ordered AG-groupoids by the properties of fuzzy left (right, quasi-, bi-, generalized bi-) ideals We will characterize regular (resp. intra-regular, both regular and intra-regular) ordered AG-groupoids by the properties of fuzzy left (right, quasi-, bi-, generalized bi-) ideals
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