Bi-interior ideals of Γ-semirings

Constructive counterparts of some interior ideals in a co-quasiordered semigroup

“…(a) Let x, y ∈ S such that xy ∈ i∈I K i . Then there exists an index (15). This means that the set i∈I K i is a co-ideal of S.…”

“…Let S be a semigroup. The concept of (left, right) quasiinterior ideals was analyzed in papers [14][15][16] by M. M. Krishna Rao:…”

“…W. Jantanan, O. Johdee and N. Praththong in [8] and M. M. Krishna Rao in [14] also wrote about interior ideals in ordered semigroup. The concepts of weak-interior ideals and quasi-interior ideals were introduced in articles [15,16] by M. M. Krishna Rao. D. A. Romano has analyzed the concepts of weak-interior ideals and quasi-interior ideals in ordered semigroups ( [24]).…”

Vague Bi-Quasi-Interior Ideals of Γ-Semirings

“…Many mathematicians proved important results and characterization of algebraic structures by using the concept and the properties of a generalization of ideals in algebraic structures. Rao et al [9,11,12] introduced the concepts of left (resp., right) bi-quasi-ideals and bi-interior ideals of Γ-semirings and studied the properties of left bi-quasi ideals. However, Bhargavi et al [1][2][3][4][5][6]8] developed the theory of vague sets on Γ-semirings.…”

A Study of r-Ideals, K-Ideals and m−k Ideals of Ordered Semirings

“…Iseki [4,5,6] introduced the concept of quasi ideal for semirings. Murali Krishna Rao [13,14] introduced the concept of biinterior ideal for a semigroup and a Γ−semiring as a generalization of quasi ideal, bi-ideal and interior ideal Shabir et al [31] studied ideals in semigroups.Murali Krishna Rao [10,11,12] studied ideals of Γ−semirings. Murali Krishna Rao [20][21][22] introduced the notion of left (right) bi-quasi ideal of semiring, Γ−semiring,Γ−semigroup and studied the properties of left bi-quasi ideals and characterized the left bi-quasi simple Γ−semigroup and regular Γ−semigroup using left bi-quasi ideals of Γ−semigroup Murali Krishna Rao [17,18] introduced the notion of bi-quasi-interior ideal as a generalization of quasi ideal, bi-ideal and interior ideal of Γ−semiring and studied their properties.…”