Publication: Kasch modules and pV-rings
Issued Date
2005-01-01
Resource Type
ISSN
10053867
Other identifier(s)
2-s2.0-14644414210
Rights
Mahidol University
Rights Holder(s)
SCOPUS
Bibliographic Citation
Algebra Colloquium. Vol.12, No.2 (2005), 219-227
Suggested Citation
Sergio R. López-Permouth, K. P. Shum, Nguyen Van Sanh Kasch modules and pV-rings. Algebra Colloquium. Vol.12, No.2 (2005), 219-227. doi:10.1142/S1005386705000210 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/16647
Research Projects
Organizational Units
Authors
Journal Issue
Thesis
Title
Kasch modules and pV-rings
Other Contributor(s)
Abstract
Let R be a ring. A right R-module M is called p-injective if every homomorphism from a principal right ideal of R to M can be given by a left multiplication. A ring R is called a right pV-ring if every simple R-module is p-injective. In this paper, Kasch modules are considered. It is proved that if a Kasch module M is finitely generated and quasi-p-injective, then there is a bijective correspondence between the class of maximal submodules of M and the class of all minimal left ideals of its endomorphism ring. Also, it is proved that if M is a pV-module which is a finitely generated projective self-generator, then its endomorphism ring is a right pV-ring. Finally, it is proved that being a right or left pV-ring is a Morita, invariant. © 2005 AMSS CAS & Suzhou Univ.