A study of a generalization of bi-ideal, quasi ideal and interior ideal of semigroup

In this paper, as a further generalization of ideals, we introduce the notion of bi- quasi-interior ideals as a generalization of bi ideal, quasi ideal, interior ideal, bi-interior ideal and bi-quasi ideal of semigroup and study the properties of bi-quasi-interior ideals of semigroup

(f, g)-derivation of ordered Γ-semirings

In this paper, we introduce the concept of (f, g)-derivation, which is a generalization of f- derivation and derivation of ordered Γ-semiring and study some properties of (f, g)-derivation of ordered Γ-semirings. We prove that, if d is a (f, g)-derivation of an ordered integral Γ-semiring M then ker d is a m-k-ideal of M and we characterize m-k-ideal using (f, g)-derivation of ordered Γ-semiring M

Derivation dα,β of ordered G-semirings

In this paper, we introduce the concept of derivation dα,β of ordered G-semiring. We study some of the properties of derivation dα,β of ordered G-semirings. We prove that if a derivation dα,β is nonzero on an integral G-semiring M then it is non-zero on any non-zero ideal of M and we characterize k-ideal and m - k ideal using derivation dα,β of ordered G-semiring

Г-Field

In this paper, we introduce the notion of a Г-field as a generalization of field, study them properties of a Г -field and prove that M is a Г-field if and only if M is an integral, simple and commutative Г-ring

Ideals in Ordered Γ-Semirings

In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal in ordered Γ-semirings, study the properties of ideals in ordered Γ-semirings and the relations between them. We characterize m − k ideals using derivation of ordered Γ-semirings and prove that every ideal in a mono regular ordered Γ-semiring is a prime ideal and field ordered Γ-semiring is simple

On Γ-Semiring With Identity

In this paper we study the properties of structures of the semigroup (M,+) and the Γ-semigroup M of Γ -semiring M and regular Γ-semiring M satisfying the identity a + aαb = a or aαb + a = a or a + aαb + b = a or a + 1 = 1, for all a ∈ M, α ∈ Γ. We also study the properties of Γ-semiring with unity 1 which is also an additive identity

Fuzzy Prime Ideals in Ordered Г-Semirings

We introduce the notion of ideal, prime ideal, fuzzy ideal, fuzzyprime ideal of ordered Г -semiring and study their properties and relations between them. We characterize the prime ideals of ordered Г - semiring with respect to fuzzy ideals. And also characterize simple ordered Г - semiring with respect to fuzzy prime ideals of ordered We introduce the notion of ideal, prime ideal, fuzzy ideal, fuzz

On Field Γ−semiring and complemented Γ−semiring with identity

In this paper we study the properties of structures of the semi-group (M; +) and th

Bi-quasi Ideals and Fuzzy Bi-quasi Ideals of Semigroups

In this paper,as a further generalization of ideals, we introduce the notion of bi-quasi ideal of Г- semigroup as a generalization of bi-ideal of Г-semigroup. We study the properties of bi-quasi ideal, characterize the bi-quasi simple Г-semigroup andregular Г-semigroup using bi-quasi ideals. We introduce the notion of fuzzy bi-quasi ideal of Г-semigroup as a generalization of fuzzy bi-ideal and we characterize the regular Г-semigroup in terms of fuzzy bi-quasi ideals of Г-semigroup

Bi-Interior Ideals of Γ-Semirings

In this paper, as a further generalization of ideals, we introduce the notion of bi-interior ideal as a generalization of quasi ideal, bi-ideal and interior ideal of Γ-semiring and study the properties of bi-interior ideals of Γ-semiring. We prove that if M is a field Γ-semiring, then M is a bi-interior simple Γ-semiring