Comparisons of recollements and tilting modules

The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.     

重模代数和量子Yang-Baxter模代数的量子化

In this paper, we mainly construct quantization of dimodule algebras and quantum Yang-Baxter H-module algebras, and give some results of smash products and braided products.     

Relative global dimensions of extensions

An extension of algebras is a homomorphism of algebras preserving identities. Given an extension f:B→A, the relative global dimension of f is defined to be the supremum of relative projective dimensions of all A-modules. In this paper, we compare relative homological dimensions of two extensions of ordinary algebras under certain conditions. As an application, for any natural number n, we present a general method for constructing non-trivial extensions of Artin algebras of relative global dimension at least n.     

Rings admitting nonzero homomorphisms between non-injective modules

A variety of rings including those that are Morita equivalent to local perfect rings, two by two upper triangular matrix rings over a division ring or certain rings arising in the framework of rings described by various test modules for injectivity satisfy a common property: there is a nonzero homomorphism between any two non-injective modules. In this paper, after settling a special case inspired by a concept due to Enochs as the first step, we provide a complete characterization of the rings of the title.     

Strongly Rickart objects in abelian categories

We introduce and study (dual) strongly relative Rickart objects in abelian categories. We prove general properties, we analyze the behaviour with respect to (co)products, and we study the transfer via functors. We also give applications to Grothendieck categories, (graded) module categories and comodule categories. Our theory of (dual) strongly relative Rickart objects may be employed in order to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian categories.     

The tensor product of Gorenstein-projective modules over category algebras

For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism.