For a class of modules XX, we introduce the X X-transpose of a module with respect to a
bimodule, which unifies some well-known transposes. Let VV be a subclass of X X. The …

Let $\mathcal X $ be a subcategory of left $ S $-modules and $ _ {R} U_ {S} $ an $(R, S) $-
bimodule. As a generalization of an adjoint cotranspose, we introduce an adjoint $\mathcal …

Let S and R be rings and _SC_R be a semidualizing bimodule. We first give the definitions
of C-transpose and nC-torsionfree and give a criterion for a module A to be G_C-projective …

Let R and S be rings and RωS a semidualizing bimodule. We introduce and study the
adjoint cotransposes of modules and adjoint n-ω-cotorsionfree modules. We show that the …

Let A be a ring and M an AA-bimodule. Any left module over the trivial extension A⋉ M is
corresponds to a pair (X, ϕ) where X is a left A-module and ϕ is an A-morphism from M⊗ AX …

In this paper, we give a relationship between projective generators (resp., injective
cogenerators) in the category of R-modules and the counterparts in the category of …

Let A/S be a ring extension with S commutative. We prove that ω⊗ S AA is a generalized
tilting module if ωS is a generalized tilting module. In this case, we obtain that⊥ ω-resol …

X -INJECTIVE AND GORENSTEIN X -INJECTIVE MODULES Page 1 Far East Journal of
Mathematical Sciences (FJMS) © 2014 Pushpa Publishing House, Allahabad, India …

Let R⋉ M be a trivial extension of a ring R by an RR-bimodule M. We first study the transfer
of some rings such as left V-rings, left Kasch rings, left PS rings between R and R⋉ M. Then …

Let R be a left and right Noetherian ring. In this paper, we prove that any Gorenstein
transpose of a finitely generated R-module is exactly an Auslander transpose. As …