• 제목/요약/키워드: graded rings

검색결과 31건 처리시간 0.023초

DECOMPOSITIONS OF GRADED MAXIMAL SUBMODULES

  • Moh'd, Fida
    • 대한수학회논문집
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    • 제37권1호
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    • pp.1-15
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    • 2022
  • In this paper, we present different decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems.

GROUP GRADED TYPES OF BÉZOUT MODULES

  • Ahmed, Mamoon;Moh'D, Fida
    • 대한수학회논문집
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    • 제32권3호
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    • pp.523-534
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    • 2017
  • In this paper, we introduce two group graded types of $B{\acute{e}}zout$ modules, namely graded-$B{\acute{e}}zout$ modules and weakly graded-$B{\acute{e}}zout$ modules, which are two $B{\acute{e}}zout$ versions in Graded Module Theory. We investigate the relationship among the three types of $B{\acute{e}}zout$ modules, the ordinary $B{\acute{e}}zout$ modules and the two graded types of $B{\acute{e}}zout$ modules. Also, we study the structure of these new $B{\acute{e}}zout$ modules along with different properties; for instance, "A graded-$B{\acute{e}}zout$ R-module, with R being a Noetherian ring, is Noetherien iff it is gr-Noetherian".

DEPTHS OF THE REES ALGEBRAS AND THE ASSOCIATED GRADED RINGS

  • Kim, Mee-Kyoung
    • 대한수학회보
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    • 제31권2호
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    • pp.210-214
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    • 1994
  • The purpose of this paper is to investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring g $r_{I}$(R) of an ideal I in a local ring (R,m) of dim(R) > 0. The relationship between the Cohen-Macaulayness of these two rings has been studied extensively. Let (R, m) be a local ring and I an ideal of R. An ideal J contained in I is called a reduction of I if J $I^{n}$ = $I^{n+1}$ for some integer n.geq.0. A reduction J of I is called a minimal reduction of I. The reduction number of I with respect to J is defined by (Fig.) S. Goto and Y.Shimoda characterized the Cohen-Macaulay property of the Rees algebra of the maximal ideal of a Cohen-Macaulay local ring in terms of the Cohen-Macaulay property of the associated graded ring of the maximal ideal and the reduction number of that maximal ideal. Let us state their theorem.m.m.

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Radial vibration behaviors of cylindrical composite piezoelectric transducers integrated with functionally graded elastic layer

  • Wang, H.M.;Wei, Y.K.;Xu, Z.X.
    • Structural Engineering and Mechanics
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    • 제38권6호
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    • pp.753-765
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    • 2011
  • The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

ON THE FIRST GENERALIZED HILBERT COEFFICIENT AND DEPTH OF ASSOCIATED GRADED RINGS

  • Mafi, Amir;Naderi, Dler
    • 대한수학회보
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    • 제57권2호
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    • pp.407-417
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    • 2020
  • Let (R, m) be a d-dimensional Cohen-Macaulay local ring with infinite residue field. Let I be an ideal of R that has analytic spread ℓ(I) = d, satisfies the Gd condition, the weak Artin-Nagata property AN-d-2 and m is not an associated prime of R/I. In this paper, we show that if j1(I) = λ(I/J) + λ[R/(Jd-1 :RI+(Jd-2 :RI+I):R m)] + 1, then I has almost minimal j-multiplicity, G(I) is Cohen-Macaulay and rJ(I) is at most 2, where J = (x1, , xd) is a general minimal reduction of I and Ji = (x1, , xi). In addition, the last theorem is in the spirit of a result of Sally who has studied the depth of associated graded rings and minimal reductions for m-primary ideals.

ON COLUMN INVARIANT AND INDEX OF COHEN-MACAULAY LOCAL RINGS

  • Koh, Jee;Lee, Ki-Suk
    • 대한수학회지
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    • 제43권4호
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    • pp.871-883
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    • 2006
  • We show that the Auslander index is the same as the column invariant over Gorenstein local rings. We also show that Ding's conjecture ([13]) holds for an isolated non-Gorenstein ring A satisfying a certain condition which seems to be weaker than the condition that the associated graded ring of A is Cohen-Macaulay.