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WSA -Supplements and Proper Classes

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yılmaz Mehmet Demirci & Ergül Türkmen, 2022. "WSA -Supplements and Proper Classes," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2964-:d:890244
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