• Title/Summary/Keyword: ordered quasi-ideal

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On Ordered Ternary Semigroups

  • Daddi, Vanita Rohit;Pawar, Yashashree Shivajirao
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.375-381
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    • 2012
  • We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in an ordered ternary semigroup and study their properties. Also regular ordered ternary semigroup is defined and several ideal-theoretical characterizations of the regular ordered ternary semigroups are furnished.

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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CHARACTERIZATIONS OF ORDERED INTRA k-REGULAR SEMIRINGS BY ORDERED k-IDEALS

  • Ayutthaya, Pakorn Palakawong na;Pibaljommee, Bundit
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.1-12
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    • 2018
  • We introduce the notion of ordered intra k-regular semirings, characterize them using their ordered k-ideals and prove that an ordered semiring S is both ordered k-regular and ordered intra k-regular if and only if every ordered quasi k-ideal or every ordered k-bi-ideal of S is ordered k-idempotent.

ON TRIPOLAR FUZZY IDEALS IN ORDERED SEMIGROUPS

  • NUTTAPONG WATTANASIRIPONG;NAREUPANAT LEKKOKSUNG;SOMSAK LEKKOKSUNG
    • Journal of applied mathematics & informatics
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    • v.41 no.1
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    • pp.133-154
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    • 2023
  • In this paper, we introduce the concept of tripolar fuzzy sub-semigroups, tripolar fuzzy ideals, tripolar fuzzy quasi-ideals, and tripolar fuzzy bi-ideals of an ordered semigroup and study some algebraic properties of them. Moreover, we prove that tripolar fuzzy bi-ideals and quasi-ideals coincide only in a particular class of ordered semigroups. Finally, we prove that every tripolar fuzzy quasi-ideal is the intersection of a tripolar fuzzy left and a tripolar fuzzy right ideal.

On Generalised Quasi-ideals in Ordered Ternary Semigroups

  • Abbasi, Mohammad Yahya;Khan, Sabahat Ali;Basar, Abul
    • Kyungpook Mathematical Journal
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    • v.57 no.4
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    • pp.545-558
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    • 2017
  • In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m,(p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m,(p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m,(p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

IDEAL THEORY IN ORDERED SEMIGROUPS BASED ON HESITANT FUZZY SETS

  • Ahn, Sun Shin;Lee, Kyoung Ja;Jun, Young Bae
    • Honam Mathematical Journal
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    • v.38 no.4
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    • pp.783-794
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    • 2016
  • The notions of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are introduced, and several properties are investigated. Relations between a hesitant fuzzy left (resp., right) ideal,a hesitant fuzzy bi-ideal and a hesitant fuzzy quasi-ideal are discussed. Characterizations of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are considered.

Purities of Ordered Ideals of Ordered Semirings

  • Ayutthaya, Pakorn Palakawong na;Pibaljommee, Bundit
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.455-465
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    • 2020
  • We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

Intuitionistic fuzzy interior ideals in ordered semigroup

  • Park, Chul-Hwan
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.1
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    • pp.118-122
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    • 2007
  • In this paper, we consider the intuitionistic fuzzification of the notion of a interior ideal in ordered semigroup S, and investigate some properties of such ideals. In terms of intuitionistic fuzzy set, characterizations of intuitionistic fuzzy interior ideals in ordered semigroups are discussed. Using a collection of interior ideals with additional conditions, an intuitionistic fuzzy interiror ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy interior ideals of an ordered semigroup are investigated. We also give a characterization of a intuitionistic fuzzy simple semigroup in terms of intuitionistic fuzzy interior ideals.

GENERALIZED BIPOLAR FUZZY INTERIOR IDEALS IN ORDERED SEMIGROUPS

  • Ibrar, Muhammad;Khan, Asghar;Abbas, Fatima
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.285-300
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    • 2019
  • This research focuses on the characterization of an ordered semigroups (OS) in the frame work of generalized bipolar fuzzy interior ideals (BFII). Different classes namely regular, intra-regular, simple and semi-simple ordered semigroups were characterized in term of $({\alpha},{\beta})$-BFII (resp $({\alpha},{\beta})$-bipolar fuzzy ideals (BFI)). It has been proved that the notion of $({\in},{\in}{\gamma}q)$-BFII and $({\in},{\in}{\gamma}q)$-BFI overlap in semi-simple, regular and intra-regular ordered semigroups. The upper and lower part of $({\in},{\in}{\gamma}q)$-BFII are discussed.

THE COHN-JORDAN EXTENSION AND SKEW MONOID RINGS OVER A QUASI-BAER RING

  • HASHEMI EBRAHIM
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.1-9
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    • 2006
  • A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring, G be an ordered monoid acting on R by $\beta$ and R be G-compatible. It is shown that R is (left principally) quasi-Baer if and only if skew monoid ring $R_{\beta}[G]$ is (left principally) quasi-Baer. If G is an abelian monoid, then R is (left principally) quasi-Baer if and only if the Cohn-Jordan extension $A(R,\;\beta)$ is (left principally) quasi-Baer if and only if left Ore quotient ring $G^{-1}R_{\beta}[G]$ is (left principally) quasi-Baer.