ON REFINABLE MODULES

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Published Sep 28, 2014
Burcu NÄ°ÅžANCI TÃœRKMEN
Department of Mathematics, Amasya University, İpekköy, Amasya, Turkey

Abstract

We study on cofinitely (strong) refinable modules as a proper generalization of (strongly)  refinable modules. In  this paper various properties of these modules  are developed. It is shown that  (1) every (cofinite) direct summand of a (cofinitely) refinable module is (cofinitely) refinable; (2) a module is cofinitely refinable if and only if every cofinite direct summands lift modulo every submodule of ; (3) a ring  is Rad-supplemen-ted and left refinable if and only if it is semiperfect; (4) a semilocal ring  is a left and right artinian serial ring with  if and only if every left -module is strongly refinable.

 2010 Mathematics Subject Classification. 16D10,16D40.

Key words and phrases. (strongly) refinable module,  cofinitely (strong) refinable module, semiperfect ring

How to Cite

ON REFINABLE MODULES. (2014). Asian Journal of Current Engineering and Maths, 3(5), 48-51. https://doi.org/10.15520/ajcem.2014.vol3.iss5.6.pp48-51.
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How to Cite

ON REFINABLE MODULES. (2014). Asian Journal of Current Engineering and Maths, 3(5), 48-51. https://doi.org/10.15520/ajcem.2014.vol3.iss5.6.pp48-51.