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 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 ...

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China ...

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 this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring Δ(φ,ψ) Δ (φ, ψ) and the algebras A A and B B. We prove that if Δ(φ,ψ) Δ (φ, ψ) is a Gorenstein ...

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 ...

Abstract: The conjecture proposed by J.P. Serre in 1955 saying that a projective module over a polynomial ring is free has been solved independently in 1976 by D. Quillen and A.A. Suslin. As a ...

Pytorch implementation of Projective Spatial Transformers (ProST) and training convex-shape image similarity metrics. Generalizing Spatial Transformers to Projective Geometry with Applications to ...