• Title/Summary/Keyword: projective dimension

Search Result 52, Processing Time 0.022 seconds

DING PROJECTIVE DIMENSION OF GORENSTEIN FLAT MODULES

  • Wang, Junpeng
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.6
    • /
    • pp.1935-1950
    • /
    • 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
    • Bulletin of the Korean Mathematical Society
    • /
    • v.58 no.2
    • /
    • pp.497-505
    • /
    • 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
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.6
    • /
    • pp.1523-1537
    • /
    • 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
    • Journal of the Korean Mathematical Society
    • /
    • v.57 no.4
    • /
    • pp.1005-1018
    • /
    • 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
    • Communications of the Korean Mathematical Society
    • /
    • v.16 no.2
    • /
    • pp.265-275
    • /
    • 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.

  • PDF

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
    • Bulletin of the Korean Mathematical Society
    • /
    • v.40 no.4
    • /
    • pp.613-631
    • /
    • 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
    • Bulletin of the Korean Mathematical Society
    • /
    • v.35 no.4
    • /
    • pp.785-790
    • /
    • 1998
  • Using spectral sequences we calculate the hightest non-vanishing index of Tor for modules of finite projective dimension.

  • PDF