• Title/Summary/Keyword: ordered right ideal

Search Result 24, Processing Time 0.02 seconds

On Ordered Ternary Semigroups

  • Daddi, Vanita Rohit;Pawar, Yashashree Shivajirao
    • Kyungpook Mathematical Journal
    • /
    • v.52 no.4
    • /
    • pp.375-381
    • /
    • 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 PRIME LEFT(RIGHT) IDEALS OF GROUPOIDS-ORDERED GROUPOIDS

  • Lee, S.K.
    • Korean Journal of Mathematics
    • /
    • v.13 no.1
    • /
    • pp.13-18
    • /
    • 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.

  • PDF

ON SIMPLE LEFT, RIGHT AND TWO-SIDED IDEALS OF AN ORDERED SEMIGROUP HAVING A KERNEL

  • Changphas, Thawhat
    • Bulletin of the Korean Mathematical Society
    • /
    • v.51 no.4
    • /
    • pp.1217-1227
    • /
    • 2014
  • The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup ($S,{\cdot},{\leq}$) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L' of ($S,{\cdot},{\leq}$), I is properly contained in L' and L' is contained in L imply L' = L. The notions of simple right and two-sided ideals are defined similarly. In this paper, the author characterize when an ordered semigroup having a kernel is the class sum of its simple left, right and two-sided ideals. Further, the structure of simple two-sided ideals will be discussed.

INTUITIONISTIC FUZZY IDEALS IN ORDERED SEMIGROUPS

  • Khan, Asghar;Khan, Madad;Hussain, Saqib
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.1_2
    • /
    • pp.311-324
    • /
    • 2010
  • We prove that a regular ordered semigroup S is left simple if and only if every intuitionistic fuzzy left ideal of S is a constant function. We also show that an ordered semigroup S is left (resp. right) regular if and only if for every intuitionistic fuzzy left(resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ for every $a\;{\in}\;S$. Further, we characterize some semilattices of ordered semigroups in terms of intuitionistic fuzzy left(resp. right) ideals. In this respect, we prove that an ordered semigroup S is a semilattice of left (resp. right) simple semigroups if and only if for every intuitionistic fuzzy left (resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ and $\mu_A(ab)\;=\;\mu_A(ba)$, $\gamma_A(ab)\;=\;\gamma_A(ba)$ for all a, $b\;{\in}\;S$.

ON INTRA-REGULAR ORDERED SEMIGROUPS

  • Lee, D.M.;Lee, S.K.
    • Korean Journal of Mathematics
    • /
    • v.14 no.1
    • /
    • pp.95-100
    • /
    • 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.

  • PDF

Purities of Ordered Ideals of Ordered Semirings

  • Ayutthaya, Pakorn Palakawong na;Pibaljommee, Bundit
    • Kyungpook Mathematical Journal
    • /
    • v.60 no.3
    • /
    • pp.455-465
    • /
    • 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.

IDEAL THEORY IN ORDERED SEMIGROUPS BASED ON HESITANT FUZZY SETS

  • Ahn, Sun Shin;Lee, Kyoung Ja;Jun, Young Bae
    • Honam Mathematical Journal
    • /
    • v.38 no.4
    • /
    • pp.783-794
    • /
    • 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.

ON TRIPOLAR FUZZY IDEALS IN ORDERED SEMIGROUPS

  • NUTTAPONG WATTANASIRIPONG;NAREUPANAT LEKKOKSUNG;SOMSAK LEKKOKSUNG
    • Journal of applied mathematics & informatics
    • /
    • v.41 no.1
    • /
    • pp.133-154
    • /
    • 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.

INTUITIONISTIC FUZZY SEMIPRIME IDEALS OF ORDERED SEMIGROUPS

  • Kim, Kyung Ho
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.22 no.2
    • /
    • pp.235-243
    • /
    • 2009
  • In this paper, we introduce the notion of intuitionistic fuzzy semiprimality in an ordered semigroup, which is an extension of fuzzy semiprimality and investigate some properties of intuitionistic fuzzification of the concept of several ideals.

  • PDF