WSA-Supplements and Proper Classes
MATHEMATICS, cilt.10, sa.16, 2022 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 10 Sayı: 16
- Basım Tarihi: 2022
- Doi Numarası: 10.3390/math10162964
- Dergi Adı: MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Anahtar Kelimeler: proper class of short exact sequences, wsa-supplement submodule, weakly semiartinian module, C-ring, CC-ring
- Abdullah Gül Üniversitesi Adresli: Evet
Özet
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 boolean AND 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 CC-rings as a generalization of C-rings and show that a ring is a right CC-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 CC-rings.