Dual Kasch rings

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Büyükasik, E (Author) Other; Christian Lomp (Author) FCUP; Yurtsever, HB (Author) Other

Journal

Title: Journal of Algebra and its Applications

ISSN: 0219-4988

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Y-FPW

DOI: 10.1142/s0219498824502256

Abstract (EN): It is well known that a ring R is right Kasch if each simple right R-module embeds in a projective right R-module. In this paper we study the dual notion and call a ring R right dual Kasch if each simple right R-module is a homomorphic image of an injective right R-module. We prove that R is right dual Kasch if and only if every finitely generated projective right R-module is coclosed in its injective hull. Typical examples of dual Kasch rings are self-injective rings, V-rings and commutative perfect rings. Skew group rings of dual Kasch rings by finite groups are dual Kasch if the order of the group is invertible. Many examples are given to separate the notion of Kasch and dual Kasch rings. It is shown that commutative Kasch rings are dual Kasch, and a commutative ring with finite Goldie dimension is dual Kasch if and only if it is a classical ring (i.e. every element is a zero divisor or invertible). We obtain that, for a field k, a finite dimensional k-algebra is right dual Kasch if and only if it is left Kasch. We also discuss the rings over which every simple right module is a homomorphic image of its injective hull, and these rings are termed strongly dual Kasch.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17