• Title/Summary/Keyword: finite R-module

Search Result 66, Processing Time 0.027 seconds

Finite-element modeling and analysis of time-dependent thermomechanical distortion of optical sheets in a LCD module

  • Lee, Jae-Won;Hwang, Hak-Mo;Chung, In-Jae
    • 한국정보디스플레이학회:학술대회논문집
    • /
    • 2006.08a
    • /
    • pp.1436-1441
    • /
    • 2006
  • Each type of optical sheets in a LCD module experiences a characteristic behavior for thermal loading and unloading. During thermal cycling, a polymeric behavior is reversible and recyclable, depending on a material stiffness critically affected by temperature and time. Some critical issues on temperature- and time-dependent themomechanical deformation of the polymeric sheet are addressed by finite-element thermal results, followed by structural simulation results in this study.

  • PDF

THE PRODUCT OF MULTIPLICATION SUBMODULES

  • ATANI, SHAHABADDIN EBRAHIMI
    • Honam Mathematical Journal
    • /
    • v.27 no.1
    • /
    • pp.1-8
    • /
    • 2005
  • Let R be a commutative ring with non-zero identity. This paper is devoted to the study some of properties of the product of submodules of a multiplication module. Suppose N is a submodule of a multiplication R-module M. We give a condition which allows us to determine whether N is finitely generated when we assume some power of N is finitely generated.

  • PDF

COMINIMAXNESS OF LOCAL COHOMOLOGY MODULES WITH RESPECT TO IDEALS OF DIMENSION ONE

  • Roshan-Shekalgourabi, Hajar
    • Honam Mathematical Journal
    • /
    • v.40 no.2
    • /
    • pp.211-218
    • /
    • 2018
  • Let R be a commutative Noetherian ring, a be an ideal of R and M be an R-module. It is shown that if $Ext^i_R(R/a,M)$ is minimax for all $i{\leq}{\dim}\;M$, then the R-module $Ext^i_R(N,M)$ is minimax for all $i{\geq}0$ and for any finitely generated R-module N with $Supp_R(N){\subseteq}V(a)$ and dim $N{\leq}1$. As a consequence of this result we obtain that for any a-torsion R-module M that $Ext^i_R(R/a,M)$ is minimax for all $i{\leq}dim$ M, all Bass numbers and all Betti numbers of M are finite. This generalizes [8, Corollary 2.7]. Also, some equivalent conditions for the cominimaxness of local cohomology modules with respect to ideals of dimension at most one are given.

ON A GENERALIZATION OF ⊕-SUPPLEMENTED MODULES

  • Turkmen, Burcu Nisanci;Davvaz, Bijan
    • Honam Mathematical Journal
    • /
    • v.41 no.3
    • /
    • pp.531-538
    • /
    • 2019
  • We introduce FI-${\oplus}$-supplemented modules as a proper generalization of ${\oplus}$-supplemented modules. We prove that; (1) every finite direct sum of FI-${\oplus}$-supplemented R-modules is an FI-${\oplus}$-supplemented R-module for any ring R ; (2) if every left R-module is FI-${\oplus}$-supplemented over a semilocal ring R, then R is left perfect; (3) if M is a finitely generated torsion-free uniform R-module over a commutative integrally closed domain such that every direct summand of M is FI-${\oplus}$-supplemented, then M is a direct sum of cyclic modules.

NATURAL FILTRATIONS OF SOME PLETHYSMS

  • Kim, Young-Hie;Ko, Hyoung J.;Lee, Kyung-Ae
    • Bulletin of the Korean Mathematical Society
    • /
    • v.37 no.1
    • /
    • pp.191-207
    • /
    • 2000
  • Let R be a ommutative ring with unity and F a finite free R-module. For a nonnegative integer r, there exists a natural filtration of$S_r(S_2F)$ such that its associated graded module is isomorphic to $\Sigma_{{\lambda}{\epsilon}{\tau}_r}\;L_{\lambda}F$, where ${\Gamma}_{\gamma}$ set of partitions such that $$\mid${\lambda}$\mid$-2r,{{\widetilde}{\lambda}}-{{\widetilde}{\lambda}}_1},...,{{\widetilde}{\lambda}}_k},\;each\;{{\widetilde}{\lambda}}_t}$,is even. We call such filtrations plethysm formulas. We extend the above plethysm formula to the version of chain complexes. By plethysm formula we mean the composition of universally free functors. $Let{\emptyset}:G->F$ be a morphism of finite free R-modules. We construct the natural decomposition of $S_{r}(S_2{\emptyset})$,up to filtrations, whose associated graded complex is isomorphic to ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

  • PDF

CHARACTERIZATION OF WEAKLY COFINITE LOCAL COHOMOLOGY MODULES

  • Moharram Aghapournahr;Marziye Hatamkhani
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.3
    • /
    • pp.637-647
    • /
    • 2023
  • Let R be a commutative Noetherian ring, 𝔞 an ideal of R, M an arbitrary R-module and X a finite R-module. We prove a characterization for Hi𝔞(M) and Hi𝔞(X, M) to be 𝔞-weakly cofinite for all i, whenever one of the following cases holds: (a) ara(𝔞) ≤ 1, (b) dim R/𝔞 ≤ 1 or (c) dim R ≤ 2. We also prove that, if M is a weakly Laskerian R-module, then Hi𝔞(X, M) is 𝔞-weakly cofinite for all i, whenever dim X ≤ 2 or dim M ≤ 2 (resp. (R, m) a local ring and dim X ≤ 3 or dim M ≤ 3). Let d = dim M < ∞, we prove an equivalent condition for top local cohomology module Hd𝔞(M) to be weakly Artinian.

LOCAL COHOMOLOGY MODULES WHICH ARE SUPPORTED ONLY AT FINITELY MANY MAXIMAL IDEALS

  • Hajikarimi, Alireza
    • Journal of the Korean Mathematical Society
    • /
    • v.47 no.3
    • /
    • pp.633-643
    • /
    • 2010
  • Let a be an ideal of a commutative Noetherian ring R, M a finitely generated R-module and N a weakly Laskerian R-module. We show that if N has finite dimension d, then $Ass_R(H^d_a(N))$ consists of finitely many maximal ideals of R. Also, we find the least integer i, such that $H^i_a$(M, N) is not consisting of finitely many maximal ideals of R.

PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS

  • Xiang, Yueming
    • Communications of the Korean Mathematical Society
    • /
    • v.25 no.4
    • /
    • pp.497-510
    • /
    • 2010
  • Let R be a ring and n a fixed non-negative integer. $\cal{TI}_n$ (resp. $\cal{TF}_n$) denotes the class of all right R-modules of FGT-injective dimensions at most n (resp. all left R-modules of FGT-flat dimensions at most n). We prove that, if R is a right $\prod$-coherent ring, then every right R-module has a $\cal{TI}_n$-cover and every left R-module has a $\cal{TF}_n$-preenvelope. A right R-module M is called n-TI-injective in case $Ext^1$(N,M) = 0 for any $N\;{\in}\;\cal{TI}_n$. A left R-module F is said to be n-TI-flat if $Tor_1$(N, F) = 0 for any $N\;{\in}\;\cal{TI}_n$. Some properties of n-TI-injective and n-TI-flat modules and their relations with $\cal{TI}_n$-(pre)covers and $\cal{TF}_n$-preenvelopes are also studied.

CHARACTERIZATION OF PRIME SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A VALUATION DOMAIN

  • Mirzaei, Fatemeh;Nekooei, Reza
    • Journal of the Korean Mathematical Society
    • /
    • v.54 no.1
    • /
    • pp.59-68
    • /
    • 2017
  • Let $F=R^{(n)}$ be a free R-module of finite rank $n{\geq}2$. In this paper, we characterize the prime submodules of F with at most n generators when R is a $Pr{\ddot{u}}fer$ domain. We also introduce the notion of prime matrix and we show that when R is a valuation domain, every finitely generated prime submodule of F with at least n generators is the row space of a prime matrix.

PRIMARY DECOMPOSITION OF SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A BÉZOUT DOMAIN

  • Fatemeh Mirzaei;Reza Nekooei
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.2
    • /
    • pp.475-484
    • /
    • 2023
  • Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.