Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

In this paper we focus on a special class of commutative local‎ ‎rings called SPAP-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎We characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an SPAP-ring and derive some basic properties‎. ‎Then we answer the‎ ‎question of Lam and Reyes about strongly Oka ideals fam...

In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitabl...