• Title/Summary/Keyword: N-ideal

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A GRADED MINIMAL FREE RESOLUTION OF THE 2ND ORDER SYMBOLIC POWER OF THE IDEAL OF A STAR CONFIGURATION IN ℙn

  • Shin, Yong-Su
    • Journal of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.169-181
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    • 2019

  • In [9], Geramita, Harbourne, and Migliore find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a linear star configuration in ${\mathbb{P}}^n$ n of any codimension r. In [8], Geramita, Galetto, Shin, and Van Tuyl extend the result on a general star configuration in ${\mathbb{P}}^n$ but for codimension 2. In this paper, we find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a general star configuration in ${\mathbb{P}}^n$ of any codimension r using a matroid configuration in [10]. This generalizes both the result on a linear star configuration in ${\mathbb{P}}^n$ of codimension r in [9] and the result on a general star configuration in ${\mathbb{P}}^n$ of codimension 2 in [8].

  • https://doi.org/10.4134/JKMS.j180119 인용 PDF KSCI

ON STRONGLY QUASI PRIMARY IDEALS

  • Koc, Suat;Tekir, Unsal;Ulucak, Gulsen
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.729-743
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    • 2019

  • In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if $ab{\in}Q$ for $a,b{\in}R$ implies either $a^2{\in}Q$ or $b^n{\in}Q$ ($a^n{\in}Q$ or $b^2{\in}Q$) for some $n{\in}{\mathbb{N}}$. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph ${\Gamma}_I(R)$ and denote it by ${\Gamma}^*_I(R)$, where I is an ideal of R. We investigate the relations between ${\Gamma}^*_I(R)$ and ${\Gamma}_I(R)$. Further, we use strongly quasi primary ideals and ${\Gamma}^*_I(R)$ to characterize von Neumann regular rings.

  • https://doi.org/10.4134/BKMS.b180522 인용 PDF KSCI HTML

ON S-MULTIPLICATION RINGS

  • Mohamed Chhiti;Soibri Moindze
    • Journal of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.327-339
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    • 2023

  • Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce a new class of ring, called S-multiplication rings which are S-versions of multiplication rings. An R-module M is said to be S-multiplication if for each submodule N of M, sN ⊆ JM ⊆ N for some s ∈ S and ideal J of R (see for instance [4, Definition 1]). An ideal I of R is called S-multiplication if I is an S-multiplication R-module. A commutative ring R is called an S-multiplication ring if each ideal of R is S-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and S-P IR. Moreover, we generalize some properties of multiplication rings to S-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.

  • https://doi.org/10.4134/JKMS.j220030 인용 PDF

QUASIRETRACT TOPOLOGICAL SEMIGROUPS

  • Jeong, Won Kyun
    • Korean Journal of Mathematics
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    • v.7 no.1
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    • pp.111-116
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    • 1999

  • In this paper, we introduce the concepts of quasi retract ideals and quasi retract topological semigroups which are weaker than those of retract ideals and retract topological semigroups, respectively. We prove that every $n$-th power ideal of a commutative power cancellative power ideal topological semigroup is a quasiretract ideal.

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