Strongly noncosingular modules

Document Type : Research Paper


1 İzmir Institute of Technology‎, ‎Department‎ ‎of Mathematics‎, ‎35430‎, İzmir, Turkey.

2 Bitlis Eren University‎, ‎Department of Mathematics‎, ‎13000‎, Bitlis, ‎Turkey.


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.


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