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 ...

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 ...

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 ...

The main purpose of this paper is to prove the following result concerning Serre's problem: Any projective module of rank n over k[ X1, ⋯, Xn ] (where k is an infinite field) is free. We give also ...

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 ...