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 ...

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 ...

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 ...

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 ...

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 ...

In this task we were asked to do affine transformation. Affine transfomation could do the following transformation simultaneously. Scalling Rotation Shearing Translation And then we were asked to do ...

In this project, I use SIFT and Projective Structure from Motion to automatically recover the 3D structure from part of the given images. The procedures as below are followed: 1, Image process: read ...