STRONGLY NONCOSINGULAR MODULES


Alagoz Y. , Durgun Y.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, cilt.42, ss.999-1013, 2016 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Cilt numarası: 42 Konu: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1182/blood-2016-07-726547
  • Dergi Adı: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.999-1013

Özet

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.