A Note on Abelian Categories of Cofinite Modules

A Note on Finsler Modules

Abelian Categories of Modules over a (Lax) Monoidal Functor

In [CY98] Crane and Yetter introduced a deformation theory for monoidal categories. The related deformation theory for monoidal functors introduced by Yetter in [Yet98] is a proper generalization of Gerstenhaber’s deformation theory for associative algebras [Ger63, Ger64, GS88]. In the present paper we solidify the analogy between lax monoidal functors and associative algebras by showing that u...

on direct sums of baer modules

the notion of baer modules was defined recently

A note on primary-like submodules of multiplication modules

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

Gorenstein projective objects in Abelian categories

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...