Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/6176
Title: Strongly noncosingular modules
Authors: Alagöz, Yusuf
Durğun, Yılmaz
Keywords: R-modules
Rings
Coatomic modules
Coclosed submodules
Modules (Algebra)
Issue Date: Aug-2016
Publisher: Iranian Mathematical Society
Source: Alagöz, Y., and Durğun, Y. (2016). Strongly noncosingular modules. Bulletin of the Iranian Mathematical Society, 42(4), 999-1013.
Abstract: An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3) absolutely coneat modules are strongly noncosingular if and only if R is a right max ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.
URI: http://hdl.handle.net/11147/6176
ISSN: 1735-8515
1017-060X
1018-6301
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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