In this paper, we characterize when the radical $\sqrt{I}$ of every interior ideal $I$ a semigroup $S$ is subsemigroup $S$. Also, (or right or left quasi-ideal bi-ideal subsemigroup) an bi-ideal)

Notions of strongly regular, regular and left(right) regular $Gamma$−semigroupsare introduced. Equivalent conditions are obtained through fuzzy notion for a$Gamma$−semigroup to be either strongly regular or regular or left regular.

There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

We show that every quasi-ordinary Weierstrass polynomial P (Z) = Z + a1(X)Z d−1 + · · ·+ ad(X) ∈ K[[X]][Z], X = (X1, . . . , Xn), over an algebraically closed field of characterisic zero K, such that a1 = 0, is ν-quasi-ordinary. That means that if the discriminant ∆P ∈ K[[X]] is equal to a monomial times a unit then the ideal (a i (X))i=2,...,d is monomial and generated by one of a i (X). We us...

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasistability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existen...

We initiate the study of interval-valued fuzzy quasi-ideal of a semigroup. In Section 2, we list some basic definitions in the later sections. In Section 3, we investigate interval-valued fuzzy subsemigroups and in Section 4, we define intervalvalued fuzzy quasi-ideals and establish some of their basic properties. In Section 5, we obtain characterizations of regular and intraregular semigroups ...

This paper concerns curves on non-commutative schemes, hereafter called quasi-schemes. A quasi-scheme X is identiied with the category ModX of quasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embedded hypersurface Y. Let C be a curve on X which is in \good posi-tion" with respect to Y (see Deenition 5.1)|this deenition includes a requirement that X be far from commutativ...

Fuzzy ideal set and fuzzy local function of fuzzy ideals with fuzzy topologies were introduced and studied by D. Sarker [10]. The purpose of this paper deals with new sort of fuzzy ideal and fuzzy local function namely fuzzy ideal and r-fuzzy open local function. Many of its characterizations, properties and connections between it and other corresponding fuzzy notions are studied. Also, we intr...