• Title/Summary/Keyword: right ideals

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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.

One-sided Prime Ideals in Semirings

  • Shabir, Muhammad;Iqbal, Muhammad Sohail
    • Kyungpook Mathematical Journal
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    • v.47 no.4
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    • pp.473-480
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    • 2007
  • In this paper we define prime right ideals of semirings and prove that if every right ideal of a semiring R is prime then R is weakly regular. We also prove that if the set of right ideals of R is totally ordered then every right ideal of R is prime if and only if R is right weakly regular. Moreover in this paper we also define prime subsemimodule (generalizing the concept of prime right ideals) of an R-semimodule. We prove that if a subsemimodule K of an R-semimodule M is prime then $A_K(M)$ is also a prime ideal of R.

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ON RINGS WHOSE ESSENTIAL MAXIMAL RIGHT IDEALS ARE GP-INJECTIVE

  • Jeong, Jeonghee;Kim, Nam Kyun
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.399-407
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    • 2022
  • In this paper, we continue to study the von Neumann regularity of rings whose essential maximal right ideals are GP-injective. It is proved that the following statements are equivalent: (1) R is strongly regular; (2) R is a 2-primal ring whose essential maximal right ideals are GP-injective; (3) R is a right (or left) quasi-duo ring whose essential maximal right ideals are GP-injective. Moreover, it is shown that R is strongly regular if and only if R is a strongly right (or left) bounded ring whose essential maximal right ideals are GP-injective. Finally, we prove that a PI-ring whose essential maximal right ideals are GP-injective is strongly π-regular.

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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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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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.

ON PRIME LEFT(RIGHT) IDEALS OF GROUPOIDS-ORDERED GROUPOIDS

  • Lee, S.K.
    • Korean Journal of Mathematics
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    • v.13 no.1
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    • pp.13-18
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    • 2005
  • Recently, Kehayopulu and Tsingelis studied for prime ideals of groupoids-ordered groupoids. In this paper, we give some results on prime left(right) ideals of groupoid-ordered groupoid. These results are generalizations of their results.

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PRIME BI-IDEALS OF GROUPOIDS

  • Lee, S.K.
    • Korean Journal of Mathematics
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    • v.13 no.2
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    • pp.217-221
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    • 2005
  • Kehayopulu and Tsingelis [2] studied prime ideals of groupoids. Also the author studied prime left (right) ideals of groupoids. In this paper, we give some results on prime bi-ideals of groupoids.

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