A-D3 Modules and A-D4 Modules

Zhanmin Zhu and Carmelo Antonio Finocchiaro

Journal of Mathematics, 2023, vol. 2023, 1-7

Abstract: Let A be a class of some right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A-D3 if, whenever N and K are direct summands of M with M=N+K and M/K∈A, then N∩K is also a direct summand of M; M is called an A-D4 module, if whenever M=B⊕A where B and A are submodules of M and A∈A, then every epimorphism f:B⟶A splits. Several characterizations and properties of these classes of modules are investigated. As applications, some new characterizations of semisimple Artinian rings, quasi-Frobenius rings, von Neumann regular rings, semiregular rings, perfect rings, semiperfect rings, hereditary rings, semihereditary rings, and PP rings are given.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2023/4148088.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2023/4148088.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4148088

DOI: 10.1155/2023/4148088

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().