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December, 2017 Coreflexive Modules and Semidualizing Modules with Finite Projective Dimension
Xi Tang, Zhaoyong Huang
Taiwanese J. Math. 21(6): 1283-1324 (December, 2017). DOI: 10.11650/tjm/8009

Abstract

Let $R$ and $S$ be rings and $_S\omega_R$ a semidualizing bimodule. For a subclass $\mathcal{T}$ of the class of $\omega$-coreflexive modules and $n \geq 1$, we introduce and study modules of $\omega$-$\mathcal{T}$-class $n$. By using the properties of such modules, we get some equivalent characterizations for $\omega_S$ having finite projective dimension. In particular, we prove that the projective dimension of $\omega_S$ is at most $n$ if and only if any module of $\omega$-$\mathcal{T}$-class $n$ is $\omega$-coreflexive. Moreover, we get some equivalent characterizations for $\omega_S$ having finite projective dimension at most two or one in terms of the properties of (adjoint) $\omega$-coreflexive and $\omega$-cotorsionless modules. Finally, we give some partial answers to the Wakamatsu tilting conjecture.

Citation

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Xi Tang. Zhaoyong Huang. "Coreflexive Modules and Semidualizing Modules with Finite Projective Dimension." Taiwanese J. Math. 21 (6) 1283 - 1324, December, 2017. https://doi.org/10.11650/tjm/8009

Information

Received: 1 November 2016; Revised: 19 February 2017; Accepted: 21 February 2017; Published: December, 2017
First available in Project Euclid: 17 August 2017

zbMATH: 06871370
MathSciNet: MR3732907
Digital Object Identifier: 10.11650/tjm/8009

Subjects:
Primary: 16E10, 16E30, 18G25

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 6 • December, 2017
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