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 ...

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 ...

Proceedings of the American Mathematical Society, Vol. 132, No. 6 (Jun., 2004), pp. 1613-1619 (7 pages) We show that the projective module P over a cellular algebra is injective if and only if the ...

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: It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules.

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 ...