• 제목/요약/키워드: semiprime

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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 ORTHOGONAL REVERSE DERIVATIONS OF SEMIPRIME 𝚪-SEMIRINGS

  • Kim, Kyung Ho
    • 충청수학회지
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    • 제35권2호
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    • pp.115-124
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    • 2022
  • In this paper, we introduce the notion of orthogonal reserve derivation on semiprime 𝚪-semirings. Some characterizations of semiprime 𝚪-semirimgs are obtained by means of orthogonal reverse derivations. We also investigate conditions for two reverse derivations on semiprime 𝚪-semiring to be orthogonal.

SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES

  • Lee, Sang-Cheol;Varmazyar, Rezvan
    • 대한수학회지
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    • 제49권2호
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    • pp.435-447
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    • 2012
  • Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

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.

ON 𝜙-SEMIPRIME SUBMODULES

  • Ebrahimpour, Mahdieh;Mirzaee, Fatemeh
    • 대한수학회지
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    • 제54권4호
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    • pp.1099-1108
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    • 2017
  • Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let S(M) be the set of all submodules of M and ${\phi}:S(M){\rightarrow}S(M){\cup}\{{\emptyset}\}$ be a function. We say that a proper submodule P of M is a ${\phi}$-semiprime submodule if $r{\in}R$ and $x{\in}M$ with $r^2x{\in}P{\setminus}{\phi}(P)$ implies that $rx{\in}P$. In this paper, we investigate some properties of this class of sub-modules. Also, some characterizations of ${\phi}$-semiprime submodules are given.

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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SEMIPRIME NEAR-RINGS WITH ORTHOGONAL DERIVATIONS

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제13권4호
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    • pp.303-310
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    • 2006
  • M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

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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.