WSA -Supplements and Proper Classes

Yılmaz Mehmet Demirci () and Ergül Türkmen
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Yılmaz Mehmet Demirci: Department of Engineering Science, Faculty of Engineering, Abdullah Gül University, Kocasinan, Kayseri 38080, Turkey
Ergül Türkmen: Department of Mathematics, Sciences and Arts Faculty, Amasya University, Ipekköy, Amasya 05100, Turkey

Mathematics, 2022, vol. 10, issue 16, 1-12

Abstract: In this paper, we introduce the concept of wsa-supplements and investigate the objects of the class of short exact sequences determined by wsa-supplement submodules, where a submodule U of a module M is called a wsa-supplement in M if there is a submodule V of M with U + V = M and U ∩ V is weakly semiartinian. We prove that a module M is weakly semiartinian if and only if every submodule of M is a wsa-supplement in M . We introduce C C -rings as a generalization of C -rings and show that a ring is a right C C -ring if and only if every singular right module has a crumbling submodule. The class of all short exact sequences determined by wsa-supplement submodules is shown to be a proper class which is both injectively and co-injectively generated. We investigate the homological objects of this proper class along with its relation to C C -rings.

Keywords: proper class of short exact sequences; wsa-supplement submodule; weakly semiartinian module; C -ring; CC -ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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