• Title/Summary/Keyword: left ideals

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QUASI AND BI IDEALS IN LEFT ALMOST RINGS

  • Hussain, Fawad;Khan, Walayat;Khan, Muhammad Sajjad Ali;Abdullah, Saleem
    • Honam Mathematical Journal
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    • v.41 no.3
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    • pp.449-461
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    • 2019
  • The aim of this paper is to extend the concept of quasi and bi-ideals from left almost semigroups to left almost rings which are the generalization of one sided ideals. Further, we discuss quasi and bi-ideals in regular left almost rings and intra regular left almost rings. We then explore many interesting and elegant properties of quasi and bi-ideals.

CUBIC IDEALS IN SEMIGROUPS

  • Jun, Young Bae;Khan, Asghar
    • Honam Mathematical Journal
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    • v.35 no.4
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    • pp.607-623
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    • 2013
  • Operational properties of cubic sets are first investigated. The notion of cubic subsemigroups and cubic left (resp. right) ideals are introduced, and several properties are investigated. Relations between cubic subsemigroups and cubic left (resp. right) ideals are discussed. Characterizations of cubic left (resp. right) ideals are considered, and how the images or inverse images of cubic subsemigroups and cubic left (resp. right) ideals become cubic subsemigroups and cubic left (resp. right) ideals, respectively, are studied.

GENERAL TYPES OF (α,β)-FUZZY IDEALS OF HEMIRINGS

  • Jun, Y.B.;Dudek, W.A.;Shabir, M.;Kang, Min-Su
    • Honam Mathematical Journal
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    • v.32 no.3
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    • pp.413-439
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    • 2010
  • W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

Interval-valued Fuzzy Ideals and Bi-ideals of a Semigroup

  • Cheong, Min-Seok;Hur, Kul
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.4
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    • pp.259-266
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    • 2011
  • We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

INTUITIONISTIC FUZZY IDEALS AND BI-IDEALS

  • HUR, KUL;KIM, KWANG JIN;SONG, HYEONG KEE
    • Honam Mathematical Journal
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    • v.26 no.3
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    • pp.309-330
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    • 2004
  • In this paper, we apply the concept of intuitionistic fuzzy sets to theory of semigroups. We give some properties of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

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A STUDY ON WEAK BI-IDEALS OF NEAR-RINGS

  • Cho, Yong-Uk
    • East Asian mathematical journal
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    • v.24 no.2
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    • pp.145-149
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    • 2008
  • From the notion of bi-ideals in near-rings, various generalizations of regularity conditions have been studied. In this paper, we generalize further the notion of bi-ideals and introduce the notion of weak bi-ideals in near-rings and obtain some characterizations using this concept in left self distributive near-rings.

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ON INTRA-REGULAR ORDERED SEMIGROUPS

  • Lee, D.M.;Lee, S.K.
    • Korean Journal of Mathematics
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    • v.14 no.1
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    • pp.95-100
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    • 2006
  • In this paper we give some new characterizations of the intra-regular ordered semigroups in terms of bi-ideals and quasi-ideals, bi-ideals and left ideals, bi-ideals and right ideals of ordered semigroups.

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On SF-rings and Regular Rings

  • Subedi, Tikaram;Buhphang, Ardeline Mary
    • Kyungpook Mathematical Journal
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    • v.53 no.3
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    • pp.397-406
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    • 2013
  • A ring R is called a left (right) SF-ring if simple left (right) R-modules are flat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In this paper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular; (b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regular if maximal essential right (left) ideals of R are weakly left (right) ideals of R (this result gives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring R is strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right) ideal of R which is a W-ideal; (3) if R is a left SF-ring such that $l(x)(r(x))$ is an essential left (right) ideal for every right (left) zero divisor x of R, then R is a division ring.

A NOTE OF PI-RINGS WITH RESTRICTED DESCENDING

  • Hong, Chan-Yong
    • The Pure and Applied Mathematics
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    • v.1 no.1
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    • pp.1-6
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    • 1994
  • In this paper, some properties for a PI-ring satisfying the descending chain condition on essential left ideals are studied: Let R be a ring with a polynomial identity satisfying the descending chain condition on essential ideals. Then all minimal prime ideals in R are maximal ideals. Moreover, if R has only finitely many minimal prime ideals, then R is left and right Artinian. Consequently, if every primeideal of R is finitely generated as a left ideal, then R is left and right Artinian. A finitely generated PI-algebra over a commutative Noetherian ring satisfying the descending chain condition on essential left ideals is a finite module over its center.(omitted)

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INTUITIONISTIC(S,T)-FUZZY h-IDEALS OF HEMIRINGS

  • Zhan, Jianming;Shum, K.P.
    • East Asian mathematical journal
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    • v.22 no.1
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    • pp.93-109
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    • 2006
  • The concept of intuitionistic fuzzy set was first introduced by Atanassov in 1986. In this paper, we define the intuitionistic(S,T)-fuzzy left h-ideals of a hemiring by using an s-norm S and a t-norm T and study their properties. In particular, some results of fuzzy left h-ideals in hemirings recently obtained by Jun, $\"{O}zt\"{u}rk$, Song, and others are extended and generalized to intuitionistic (S,T)-fuzzy ideals over hemirings.

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