Totally reflexive modules with respect to a semidualizing bimodule

Zhen Zhang; Xiaosheng Zhu; Xiaoguang Yan

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 385-402
  • ISSN: 0011-4642

Abstract

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Let S and R be two associative rings, let S C R be a semidualizing ( S , R ) -bimodule. We introduce and investigate properties of the totally reflexive module with respect to S C R and we give a characterization of the class of the totally C R -reflexive modules over any ring R . Moreover, we show that the totally C R -reflexive module with finite projective dimension is exactly the finitely generated projective right R -module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting.

How to cite

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Zhang, Zhen, Zhu, Xiaosheng, and Yan, Xiaoguang. "Totally reflexive modules with respect to a semidualizing bimodule." Czechoslovak Mathematical Journal 63.2 (2013): 385-402. <http://eudml.org/doc/260690>.

@article{Zhang2013,
abstract = {Let $S$ and $R$ be two associative rings, let $ _\{S\}C_\{R\}$ be a semidualizing $(S,R)$-bimodule. We introduce and investigate properties of the totally reflexive module with respect to $_\{S\}C_\{R\}$ and we give a characterization of the class of the totally $C_\{R\}$-reflexive modules over any ring $R$. Moreover, we show that the totally $C_\{R\}$-reflexive module with finite projective dimension is exactly the finitely generated projective right $R$-module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting.},
author = {Zhang, Zhen, Zhu, Xiaosheng, Yan, Xiaoguang},
journal = {Czechoslovak Mathematical Journal},
keywords = {semidualizing bimodule; totally reflexive module; Bass class; precover; preenvelope; semidualizing bimodules; totally reflexive modules; Bass classes; precovers; preenvelopes; projective resolutions; projective dimension},
language = {eng},
number = {2},
pages = {385-402},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Totally reflexive modules with respect to a semidualizing bimodule},
url = {http://eudml.org/doc/260690},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Zhang, Zhen
AU - Zhu, Xiaosheng
AU - Yan, Xiaoguang
TI - Totally reflexive modules with respect to a semidualizing bimodule
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 385
EP - 402
AB - Let $S$ and $R$ be two associative rings, let $ _{S}C_{R}$ be a semidualizing $(S,R)$-bimodule. We introduce and investigate properties of the totally reflexive module with respect to $_{S}C_{R}$ and we give a characterization of the class of the totally $C_{R}$-reflexive modules over any ring $R$. Moreover, we show that the totally $C_{R}$-reflexive module with finite projective dimension is exactly the finitely generated projective right $R$-module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting.
LA - eng
KW - semidualizing bimodule; totally reflexive module; Bass class; precover; preenvelope; semidualizing bimodules; totally reflexive modules; Bass classes; precovers; preenvelopes; projective resolutions; projective dimension
UR - http://eudml.org/doc/260690
ER -

References

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