• 제목/요약/키워드: semi-ideals

검색결과 31건 처리시간 0.027초

ON L-FUZZY SEMI-PRIME IDEALS OF A POSET AND SEPARATION THEOREMS

  • Engidaw, Derso Abeje;Alemu, Tilahun Bimerew
    • Korean Journal of Mathematics
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    • 제29권2호
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    • pp.305-320
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    • 2021
  • In this paper, the relations between L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. A result analogous to Separation Theorem is obtained using L-fuzzy semi-prime ideals.

THE WEAKLY SEMI-PRIME IDEALS OF po-Γ-SEMIGROUPS

  • Kwon, Young In;Lee, Sang Keun
    • Korean Journal of Mathematics
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    • 제5권2호
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    • pp.135-139
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    • 1997
  • We introduce the concepts of weakly prime and weakly semi-prime ideals in po-${\Gamma}$-semigroup and give some characterizations of weakly prime and weakly semi-prime ideals of po-${\Gamma}$-semigroups analogous to the characterizations of weakly prime and weakly semi-prime ideals of po-semigroups considered by N. Kehayopulu.

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INTUITIONISTIC FUZZY INTERIOR IDEALS IN ORDERED SEMIGROUPS

  • Shabir, Muhammad;Khan, A.
    • Journal of applied mathematics & informatics
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    • 제27권5_6호
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    • pp.1447-1457
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    • 2009
  • In this paper we define intuitionistic fuzzy interior ideals in ordered semigroups. We prove that in regular(resp. intra-regular and semisimple) ordered semigroups the concepts of intuitionistic fuzzy interior ideals and intuitionistic fuzzy ideals coincide. We prove that an ordered semi group is intuitionistic fuzzy simple if and only if every intutionistic fuzzy interior ideal is a constant function. We characterize intra-regular ordered semi groups in terms of interior (resp. intuitionistic fuzzy interior) ideals.

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AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS

  • Elavarasan, Balasubramanian;Porselvi, Kasi
    • 대한수학회논문집
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    • 제28권1호
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    • pp.79-85
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    • 2013
  • The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.

M-SYSTEM AND N-SYSTEM IN PO-SEMIGROUPS

  • Lee, Sang-Keun
    • East Asian mathematical journal
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    • 제19권2호
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    • pp.233-240
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    • 2003
  • Xie and Wu introduced an m-system in a po-semigroup. Kehayopulu gave characterizations of weakly prime ideals of po-semigroups and Lee and Kwon add two characterizations for weakly prime ideals. In this paper, we give a characterization of weakly prime ideals and a characterization of weakly semi-prime ideals in po-semigroups using m-system and n-system, respectively

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SOLUTION OF AN UNSOLVED PROBLEM IN BCK-ALGEBRA

  • Nisar, Farhat;Bhatti, Shaban Ali
    • East Asian mathematical journal
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    • 제21권1호
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    • pp.49-60
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    • 2005
  • In this paper we introduced Semi-neutral BCK-algebra and investigate some of its properties. The notions of ideals and subalgebras coincide in Semi-neutral BCK-algebras. We also show that if the number of nonzero elements in a Semi-neutral BCK-algebra is n, then the number of ideals/subalgebras in it is $2^n$. Further, we solved an open problem posed by W.A. Dudek in [2].

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A NEW FORM OF FUZZY GENERALIZED BI-IDEALS IN ORDERED SEMIGROUPS

  • Khan, Hidayat Ullah;Sarmin, Nor Haniza;Khan, Asghar
    • 호남수학학술지
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    • 제36권3호
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    • pp.569-596
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    • 2014
  • In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy subsystems of ordered semigroups namely (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

ON SUBMODULES INDUCING PRIME IDEALS OF ENDOMORPHISM RINGS

  • Bae, Soon-Sook
    • East Asian mathematical journal
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    • 제16권1호
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    • pp.33-48
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    • 2000
  • In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

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REDUCTIONS OF IDEALS IN COMMUTATIVE NOETHERIAN SEMI-LOCAL RINGS

  • Song, Yeong-Moo;Kim, Se-Gyeong
    • 대한수학회논문집
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    • 제11권3호
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    • pp.539-546
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    • 1996
  • The purpose of this paper is to show that the Noetherian semi-local property of the underlying ring enables us to develope a setisfactory concep of the theory of reduction of ideals in a commutative Noetherian ring.

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