• 제목/요약/키워드: semiprime ideal

검색결과 47건 처리시간 0.018초

SOME FUZZY SEMIPRIME IDEALS OF SEMIGROUPS

  • Kim, Jupil
    • 충청수학회지
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    • 제22권3호
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    • pp.459-466
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    • 2009
  • The purpose of this paper is to study the some properties of fuzzy quasi-semiprime ideal, fuzzy prime ideals and to prove some fundamental properties of semigroups. In particular, we will establish a relation between fuzzy prime ideals and weakly completely semiprime ideals by using the some equivalent conditions of fuzzy semiprime ideals.

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On the Ideal Extensions in Γ-Semigroups

  • Siripitukdet, Manoj;Iampan, Aiyared
    • Kyungpook Mathematical Journal
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    • 제48권4호
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    • pp.585-591
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    • 2008
  • In 1981, Sen [4] have introduced the concept of $\Gamma$-semigroups. We have known that $\Gamma$-semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in $\Gamma$-semigroups and characterize the relationship between the extensions of ideals and some congruences in $\Gamma$-semigroups.

ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS

  • Siripitukdet, Manoj;Iampan, Aiyared
    • 대한수학회논문집
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    • 제23권1호
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    • pp.19-27
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    • 2008
  • The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) $\Gamma$-semigroups. In 1981, Sen [8] has introduced the concept of the $\Gamma$-semigroups. We can see that any semigroup can be considered as a $\Gamma$-semigroup. The concept of ordered ideal extensions in ordered $\Gamma$-semigroups was introduced in 2007 by Siripitukdet and Iampan [12]. Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered $\Gamma$-semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered $\Gamma$-semigroups.

FULLY PRIME MODULES AND FULLY SEMIPRIME MODULES

  • Beachy, John A.;Medina-Barcenas, Mauricio
    • 대한수학회보
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    • 제57권5호
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    • pp.1177-1193
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    • 2020
  • Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module M, we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by M. We also consider the relationship between the conditions (1) M is a fully prime (semiprime) module, and (2) the endomorphism ring of M is a fully prime (semiprime) ring.

Semiprime and Semiprimary Fuzzy Ideals

  • Jeong, Tae-Eun
    • 한국지능시스템학회논문지
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    • 제9권5호
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    • pp.509-512
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    • 1999
  • We study semiprime fuzzy ideals semiprimary fuzzy ideals and their properties. We investigate that if a fuzzy ideal is semiprime and semiprimary then it is prime.

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PRIME RADICALS OF SKEW LAURENT POLYNOMIAL RINGS

  • Han, Jun-Cheol
    • 대한수학회보
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    • 제42권3호
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    • pp.477-484
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    • 2005
  • Let R be a ring with an automorphism 17. An ideal [ of R is ($\sigma$-ideal of R if $\sigma$(I).= I. A proper ideal P of R is ($\sigma$-prime ideal of R if P is a $\sigma$-ideal of R and for $\sigma$-ideals I and J of R, IJ $\subseteq$ P implies that I $\subseteq$ P or J $\subseteq$ P. A proper ideal Q of R is $\sigma$-semiprime ideal of Q if Q is a $\sigma$-ideal and for a $\sigma$-ideal I of R, I$^{2}$ $\subseteq$ Q implies that I $\subseteq$ Q. The $\sigma$-prime radical is defined by the intersection of all $\sigma$-prime ideals of R and is denoted by P$_{(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P$_{(R) is the smallest $\sigma$-semiprime ideal of R; (2) For any ring R with an automorphism $\sigma$ and for a skew Laurent polynomial ring R[x, x$^{-1}$; $\sigma$], the prime radical of R[x, x$^{-1}$; $\sigma$] is equal to P$_{(R)[x, x$^{-1}$; $\sigma$ ].

PRIME RADICALS IN ORE EXTENSIONS

  • Han, Jun-Cheol
    • East Asian mathematical journal
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    • 제18권2호
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    • pp.271-282
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    • 2002
  • Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

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INTUITIONISTIC FUZZY SEMIPRIME IDEALS OF A SEMIGROUPS

  • Ahn, Tae-Chon;Hur, Kul;Kang, Hak-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제14권3호
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    • pp.139-151
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    • 2007
  • We introduce the concept of intuitionistic fuzzy semiprimality of a semigroup which is an extension of semiprimality in it. And we obtain a characterization of a semigroup that is a semilattice of simple semigroups in terms of intuitionistic fuzzy semiprime interior ideals.

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INTUITIONISTIC FUZZY SEMIPRIME IDEALS OF ORDERED SEMIGROUPS

  • Kim, Kyung Ho
    • 충청수학회지
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    • 제22권2호
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    • pp.235-243
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    • 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.

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