Original scientific paper

On rings with one middle class of injectivity domains

Rafail Alizade ; Department of Mathematics, Yasar University, Universite Caddesi, Bornova, Izmir, Turkey
Yılmaz Mehmet Demirc ; Department of Engineering Science, Abdullah Gul University, Kocasinan, Kayseri, Turkey
Burcu Nişancı Türkmen ; Department of Mathematics, Amasya University, Ipekkoy, Amasya, Turkey
Ergül Türkmen ; Department of Mathematics, Amasya University, Ipekkoy, Amasya, Turkey

Abstract

A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper, we investigate the basic properties of modest modules.
We provide characterizations of some classes of rings using modest modules. In particular, we show that a ring having the class of crumbling modules as the only right middle class
of injectivity domains is either a right V -ring or right Noetherian; and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling
modules as the only right middle class of injectivity domains.

Keywords

injective module, poor module, modest module, SSI-ring, V -ring, W V -ring, Noetherian ring

Hrčak ID:

275698

URI

https://hrcak.srce.hr/275698

Publication date:

28.4.2022.

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