Coreflexive modules and semidualizing modules with finite projective dimension
X Tang, Z Huang - Taiwanese Journal of Mathematics, 2017 - projecteuclid.org
X Tang, Z Huang
Taiwanese Journal of Mathematics, 2017•projecteuclid.orgLet $ 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 …
$\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 …
Let and be rings and a semidualizing bimodule. For a subclass of the class of -coreflexive modules and , we introduce and study modules of --class . By using the properties of such modules, we get some equivalent characterizations for having finite projective dimension. In particular, we prove that the projective dimension of is at most if and only if any module of --class is -coreflexive. Moreover, we get some equivalent characterizations for having finite projective dimension at most two or one in terms of the properties of (adjoint) -coreflexive and -cotorsionless modules. Finally, we give some partial answers to the Wakamatsu tilting conjecture.
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