Mühendislik Bilimleri Bölümü Koleksiyonu

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Browsing Mühendislik Bilimleri Bölümü Koleksiyonu by Subject "C-ring"

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    WSA-Supplements and Proper Classes
    (MDPIST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2022) Demirci, Yilmaz Mehmet; Turkmen, Ergul; 0000-0003-3802-4211; 0000-0002-7082-1176; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Demirci, Mehmet Yılmaz
    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 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.