Quasi Ideals Research Articles

Bi-quasi-interior Ideals

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

BI-IDEALS IN TERNARY SEMINEAR RINGS

In this paper, we introduce the concept of Bi-ideal in ternary seminear rings as a generalization of quasi ideals in ternary seminear rings. We also study the notion of minimal bi-ideal in ternary seminear rings and derive some of their interesting properties.

Completely weakly, quasi-regular semigroups characterized by soft union Quasi ideals, (generalized) bi-ideals and semiprime ideals

Completely weakly, quasi-regular semigroups characterized by soft union Quasi ideals, (generalized) bi-ideals and semiprime ideals

Prime Quasi-Ideals in Ternary Seminear Rings

Objectives/Background: The ternary seminear ring is the generalization of seminear ring and it need not be a ternary semiring. Characterization of quotient ternary seminear rings and some structures of ternary seminear ring have been analysed and also studied ideals in ternary seminear rings. Further quasi ideals in ternary seminear rings defined and discussed about their properties. Methods: Properties of seminear ring and ternary semiring have been employed to carry out this research work to obtain all the characterizations of ternary seminear rings corresponding to that ternary semiring. Findings: We call an algebraic structure (T;+; :) is a ternary seminear ring if (T,+) is a Semigroup, T is a ternary semigroup under ternary multiplication and xy(z+u) = xyx+xyu for all x;y; z;u 2 T. T is said to have an absorbing zero if there exists an element 0 2 T such that x+0 = 0+x = x for all x 2 T and xy0 = x0y = 0xy = 0 for all x;y 2 T. Throughout this paper T will always stand for ternary seminear ring with an absorbing zero. In this ternary structure we try to study prime quasi ideals concept and obtain their properties. Novelty: In this study, we define the notion of Prime quasi ideals in ternary seminear rings. We also find some of their interesting results. AMS Subject Classification code: 16Y30,16Y99,17A40 Keywords: Ternary seminear ring; Idempotent ternary seminear ring; Ideals in ternary seminear ring; Quasi Ideals in ternary seminear ring; Prime Ideals in ternary seminear rings.

BI – IDEALS AND QUASI – IDEALS OF BCI ALGEBRA

In this Paper, we introduce the idea of Bi – ideals and Quasi ideals in BCI algebra. Also, we discuss the relationship between a Bi – ideal and a Quasi ideal and distinguish some properties of Bi – ideals and Quasi ideals in BCI algebra.

On Gamma LA-Rings and Gamma LA-Semirings

In this note, first we add some new results in Gamma LA-rings and then we initiate the notion of Γ-LA-semirings. Moreover, we introduce and discuss the terms left ideals, right ideals, bi-ideal, quasi ideals, almost prime and weakly almost prime ideals of a Γ-LA-semiring and their characterizations.

Bi Ideals of Nearness Semirings

Bi ideals are the generalisation of quasi ideals. In this article, it is defined that the notion of bi-ideals in semirings on weak nearness approximation spaces. Afterwards, it is explained that some of the concepts and definitions related to the subject. Also, it is given that the definition of nearness m-bi ideals and nearness (m,n)-quasi ideals. Thus, we examine the relationship between nearness m-bi ideals and nearness (m,n)-quasi ideals .

Quasi ideals of nearness semirings

This article introduces quasi-ideals in semirings on weak nearness approximation spaces. Concepts and definitions are given to clarify the subject of quasi ideals in semirings on weak nearness approximation spaces. Some basic properties of quasi ideals are also given. Furthermore, it is given that the definition of upper-near quasi ideals. And, it is examined that the relationship between quasi ideals and upper near quasi ideals. Therefore, the features described in this study will contribute greatly to the theoretical development of the nearness semirings theory.

M-ideals and its generators of ternary semigroups

The purpose of this paper is to introduce some new classes of m-bi ideals and m-quasi ideals in ternary semigroups and give some characterizations in terms of bi ideals and quasi ideals. Let U1 be the m-bi ideal of T and U2 be the m-bi ideal of U1 such that U3 2 = U2, shown that U2 is a m-bi ideal of T. Let U1, U2 and U3 be the three ternary subsemigroups of T, it has been shown that U1U2U3 is a t-bi ideal if at least one of U1, U2, U3 is l-RI or m-LATI or n-LI of T. Also we discuss m-bi ideal generated by B is < B > sub>m= B ∪ P finite

Soft covered ideals in semigroups

Abstract In this work, soft covered ideals in semigroups are constructed and in this concept, soft covered semigroups, soft covered left (right) ideals, soft covered interior ideals, soft covered (generalized) bi-ideals and soft covered quasi ideals of a semigroup are defined. Various properties of these ideals are introduced and the interrelations of these soft covered ideals and the relations of soft anti covered ideals and soft covered ideals are investigated.

Relative bi-ideals and relative quasi ideals in ordered semigroups

In this paper, after introducing the notion of relative bi-ideals and relative quasi ideals in ordered semigroups, some important properties of these bi-ideals and quasi ideals are studied. Then relatively prime and relatively weakly semiprime bi-ideals are defined and some vital results have been proved. We also define relative regularity and relative intra-regularity of an ordered semigroup and prove some results based on the connection among intra-regularity of an ordered semigroup, relative quasi and relative bi-ideals of that ordered semigroup. Finally some important results connecting relative regularity, relatively prime bi-ideals and relatively weakly semiprime bi-ideals of an ordered semigroup have also been obtained.

On various quasi ideals in $b$-semirings

On various quasi ideals in $b$-semirings

On intuitionistic fuzzy quasi ideals of rings with respect to a t-norm

On intuitionistic fuzzy quasi ideals of rings with respect to a t-norm

\(Q_1\)- fuzzy quasi ideals in semiring

The authors in [9] introduced Q1 -fuzzy set which is a natural generalization Q-fuzzy sets studied by [5, 7, 12, 13] and studied some results related to level subsets of Q1 -fuzzy set. In this study composition of two Q1 -fuzzy sets, Q1 -fuzzy points, Q1 -fuzzy quasi (prime, semiprime, irreducible, strongly irreducible) ideals are defined and revealed some related properties of these mentioned ideals. Further Q1 -fuzzy left (right) ideals generated by fuzzy points are exhibited and some quasi-ideals in terms of idempotent Q1 -fuzzy points are found.

IDEALS IN REGULAR PO - TERNARY SEMIGROUPS

The theory of ternary algebraic system was introduced by D.H. Lehmer [2] in 1932, but earlier such structures were studied by Kasner in1904, who gave the idea of n-ary algebras. In 1965, F.M. Sison [5] studied ideal theory in ternary semigroups. He also introduced the notions of regular ternary semigroups and characterized them by using the notion of quasi ideals. In 1981, the concept of  semigroups was introduced by M.K.Sen. We know that  semigroups are generalization of semigroups. The concept partially ordered  -semigroup was introduced by Y.I.Know and S.K.Lee in 1961, later it has been studied by many authors. Several researchers conducted researches on the generalizations of the notion of ideals on partially ordered  -semigroups, which play an important role in studying of ideals on partially ordered  -semigroups as well as in the study of plain semigroups. In this paper, we studied different structures of ideals in po  ternary semigroups and extended these structures in regular po  ternary semigroups.

On uni-soft (quasi) ideals of AG-groupoids

In this paper we introduced the notions of uni-soft AG-groupoids, uni-soft left(right) ideals and uni-soft quasi ideals of AG-groupoids and also investigated related properties of these structures. Some interesting Charac- terizations of uni-soft AG-groupoids and uni-soft left(right) ideals have been explored.

(λ,µ)-Fuzzy quasi-ideals and (λ,µ)-fuzzy bi-ideals in ternary semirings

In this paper we introduce the notion of (λ,µ)-Fuzzy quasi ideals and (λ,µ)-Fuzzy bi-ideals in ternary semirings which can be regarded as the generalization of fuzzy quasi ideals and fuzzy bi-ideals in ternary semirings.

Characterizations of semi-groups that are semi-lattices of left groups

Zadeh in 1965 introduce the concept of a fuzzy set which now have a wide range of applications in various fields of Engineering Sciences, Computer Science and Management Sciences. It is worth mentioning here that for applications of fuzzy sets mostly associative algebraic structures are used such as in 2003, Mordeson, Malik and Kuroki have discovered the applications of fuzzy semigroups in fuzzy coding, fuzzy finite-state machines and fuzzy languages. We have applied fuzzy set theory to associative algebraic structures and have discussed related properties. Specifically we have characterized semigroups which are semilattices of left groups by the properties of generalized fuzzy ideals. Key words: -fuzzy ideals, -fuzzy bi-ideals, -fuzzy quasi ideals.