The study of Gorenstein algebras has emerged as a cornerstone of modern algebra, offering a powerful paradigm in which duality and symmetry in module theory can be rigorously examined. These algebras ...

In many branches of mathematics, there is a clear notion of “atomic” or “indivisible” object. Examples are prime numbers, connected spaces, transitive group actions, and ergodic dynamical systems. But ...

Abstract: Aimed at that available application of smooth homomorphism is around the comparison of two smooth modulus with each other and any of its application to construct new smooth modulus has not ...

The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose ...

1 College of Science, Guilin University of Technology, Guilin, China. 2 School of Science, Guilin University of Aerospace Technology, Guilin, China. This paper aims at investigating relative Ding ...

A module M is called pseudo-projective if every epimorphism from M to each quotient module of M can be lifted to an endomorphism of M. In this paper, we study some properties of pseudo-projective ...

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, \(\mathcal{PGF}\), (respectively that of projectively coresolved Gorenstein ...

Abstract: Given a finite group G and a field k, the group ring kG decomposes into a direct sum of projective indecomposable modules and the structure of these modules is intricately tied to the ...

1 Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt &Department of Mathematics, Faculty of Science, King Abdulaziz University, KSA. In this paper we introduce and ...