• Title/Summary/Keyword: weakly prime left ideal

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WEAKLY PRIME LEFT IDEALS IN NEAR-SUBTRACTION SEMIGROUPS

  • Dheena, P.;Kumar, G. Satheesh
    • Communications of the Korean Mathematical Society
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    • v.23 no.3
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    • pp.325-331
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    • 2008
  • In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

On left, right weakly prime ideals on po-semigroups

  • Lee, Sang-Keun;Kwon, Young-In
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.315-321
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    • 1996
  • Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.

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ON WEAKLY PRIME IDEALS OF ORDERED ${\gamma}$-SEMIGROUPS

  • Kwon, Young-In;Lee, Sang-Keun
    • Communications of the Korean Mathematical Society
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    • v.13 no.2
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    • pp.251-256
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    • 1998
  • We introduce the concept of weakly prime ideals in po-$\Gamma$-semigroup and give some characterizations of weakly prime ideals.

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M-SYSTEM AND N-SYSTEM IN PO-SEMIGROUPS

  • Lee, Sang-Keun
    • East Asian mathematical journal
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    • v.19 no.2
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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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SOME ABELIAN MCCOY RINGS

  • Rasul Mohammadi;Ahmad Moussavi;Masoome Zahiri
    • Journal of the Korean Mathematical Society
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    • v.60 no.6
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    • pp.1233-1254
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    • 2023
  • We introduce two subclasses of abelian McCoy rings, so-called π-CN-rings and π-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as 2-primal rings, bounded rings etc. It is shown that a ring R is π-CN whenever every nilpotent element of index 2 in R is central. These rings naturally generalize the long-known class of CN-rings, introduced by Drazin [9]. It is proved that π-CN-rings are abelian, McCoy and 2-primal. We also show that, π-duo rings are strongly McCoy and abelian and also they are strongly right AB. If R is π-duo, then R[x] has property (A). If R is π-duo and it is either right weakly continuous or every prime ideal of R is maximal, then R has property (A). A π-duo ring R is left perfect if and only if R contains no infinite set of orthogonal idempotents and every left R-module has a maximal submodule. Our achieved results substantially improve many existing results.