Small quasi-projective modules
https://doi.org/10.26907/2949-3919.2024.3.4-28
Abstract
We study small quasi-projective modules and closely related classes of modules. The concept of a small quasi-projective module is dual to the concept of an essentially quasi-injective module, which has recently been studied in several works. It is shown that over right perfect rings, the class of small quasi-projective right modules coincides with a number of classes of right modules close to projective modules, which are studied in the article. As a consequence of the obtained results, the well-known A.A. Tuganbaev’s theorem on the coincidence of the classes of quasi-projective right modules and endomorphism-lifting right modules over right perfect rings is presented. Also, characterizations are obtained for modules M , for which in the category σ[M ] every (finitely generated, cyclic, semisimple, simple) module is small projective in σ[M ].
Keywords
essentially injective modules,
small projective modules,
small endomorphism-liftable modules,
perfect rings
Supporting agencies: The work is supported by the Russian Science Foundation (grant no. 22-21-00267).
About the Authors
А. N. Abyzov
Kazan Federal University
Russian Federation
Adel Nailevich Abyzov
Russian Federation
Adel Nailevich Abyzov
18 Kremlyovskaya str., Kazan 420008
T. D. Bui
Kazan Federal University; Can Tho University of Technology
Russian Federation
Bui Tien Dat
Russian Federation
Bui Tien Dat
18 Kremlyovskaya str., Kazan 420008
256 Nguyen Van Cu str., Can Tho, Vietnam
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Review
For citations:
Abyzov А.N., Bui T.D. Small quasi-projective modules. Mathematics and Theoretical Computer Science. 2024;2(3):4-28. (In Russ.) https://doi.org/10.26907/2949-3919.2024.3.4-28
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