Existence of Covers and Envelopes of a Left Orthogonal Class and Its Right Orthogonal Class of Modules

Arunachalam Umamaheswaran, Ramalingam Udhayakumar, Chelliah Selvaraj, Kandhasamy Tamilvanan, Masho Jima Kabeto and Ralf Meyer

Journal of Mathematics, 2022, vol. 2022, 1-12

Abstract: In this paper, we investigate the notions of X⊥-projective, X-injective, and X-flat modules and give some characterizations of these modules, where X is a class of left modules. We prove that the class of all X⊥-projective modules is Kaplansky. Further, if the class of all X-injective R-modules is contained in the class of all pure projective modules, we show the existence of X⊥-projective covers and X-injective envelopes over a X⊥-hereditary ring. Further, we show that a ring R is Noetherian if and only if W-injective R-modules coincide with the injective R-modules. Finally, we prove that if W⊆S, every module has a W-injective precover over a coherent ring, where W is the class of all pure projective R-modules and S is the class of all fp−Ω1-modules.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/8072134.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/8072134.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:8072134

DOI: 10.1155/2022/8072134

Access Statistics for this article

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