Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings

Asima Razzaque, Inayatur Rehman and Gohar Ali

Journal of Mathematics, 2022, vol. 2022, 1-8

Abstract: The LA-module is a nonassociative structure that extends modules over a nonassociative ring known as left almost rings (LA-rings). Because of peculiar characteristics of LA-ring and its inception into noncommutative and nonassociative theory, drew the attention of many researchers over the last decade. In this study, the ideas of projective and injective LA-modules, LA-vector space, as well as examples and findings, are discussed. We construct a nontrivial example in which it is proved that if the LA-module is not free, then it cannot be a projective LA-module. We also construct free LA-modules, create a split sequence in LA-modules, and show several outcomes that are connected to them. We have proved the projective basis theorem for LA-modules. Also, split sequences in projective and injective LA-modules are discussed with the help of various propositions and theorems.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/2792450.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/2792450.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:2792450

DOI: 10.1155/2022/2792450

Access Statistics for this article

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