• 제목/요약/키워드: projective dimension

검색결과 52건 처리시간 0.018초

DING PROJECTIVE DIMENSION OF GORENSTEIN FLAT MODULES

  • Wang, Junpeng
    • 대한수학회보
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    • 제54권6호
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    • pp.1935-1950
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    • 2017
  • Let R be a Ding-Chen ring. Yang [24] and Zhang [25] asked whether or not every R-module has finite Ding projective or Ding injective dimension. In this paper, we give a new characterization of that all modules have finite Ding projective and Ding injective dimension in terms of the relationship between Ding projective and Gorenstein flat modules. We also give an example to obtain negative answer to the above question.

GORENSTEIN PROJECTIVE DIMENSIONS OF COMPLEXES UNDER BASE CHANGE WITH RESPECT TO A SEMIDUALIZING MODULE

  • Zhang, Chunxia
    • 대한수학회보
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    • 제58권2호
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    • pp.497-505
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    • 2021
  • Let R → S be a ring homomorphism. The relations of Gorenstein projective dimension with respect to a semidualizing module of homologically bounded complexes between U ⊗LR X and X are considered, where X is an R-complex and U is an S-complex. Some sufficient conditions are given under which the equality ${\mathcal{GP}}_{\tilde{C}}-pd_S(S{\otimes}{L \atop R}X)={\mathcal{GP}}_C-pd_R(X)$ holds. As an application it is shown that the Auslander-Buchsbaum formula holds for GC-projective dimension.

THE u-S-GLOBAL DIMENSIONS OF COMMUTATIVE RINGS

  • Wei Qi;Xiaolei Zhang
    • 대한수학회보
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    • 제60권6호
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    • pp.1523-1537
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    • 2023
  • Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.

ON THE C-PROJECTIVE VECTOR FIELDS ON RANDERS SPACES

  • Rafie-Rad, Mehdi;Shirafkan, Azadeh
    • 대한수학회지
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    • 제57권4호
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    • pp.1005-1018
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    • 2020
  • A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹n(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

SOME CURVATURE CONDITIONS OF n-DIMENSIONAL CR-SUBMANIFOLDS OF (n-1) CR-DIMENSION IN A COMPLEX PROJECTIVE SPACE II

  • Sohn, Won-Ho
    • 대한수학회논문집
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    • 제16권2호
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    • pp.265-275
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    • 2001
  • In the previous paper we studied n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space CP(sup)(n+p)/2, and especially determined such submanifolds under curvature conditions related to vertical direction; In the present article we determine such submanifolds under curvature conditions related to horizontal directions.

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SOME CURVATURE CONDITIONS OF n-DIMENSIONAL QR-SUBMANIFOLDS OF (p-1) QR-DIMENSION IN A QUATERNIONIC PROJECTIVE SPACE QP(n+p)/4

  • Pak, Jin-Suk;Sohn, Won-Ho
    • 대한수학회보
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    • 제40권4호
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    • pp.613-631
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    • 2003
  • The purpose of this paper is to study n-dimensional QR-submanifolds of (p - 1) QR-dimension in a quaternionic projective space $QP^{(n+p)/4}$ and especially to determine such submanifolds under the curvature conditions appeared in (5.1) and (5.2).

ON THE NONVANISHING OF TOR

  • Choi, Sang-Ki
    • 대한수학회보
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    • 제35권4호
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    • pp.785-790
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    • 1998
  • Using spectral sequences we calculate the hightest non-vanishing index of Tor for modules of finite projective dimension.

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