Harmanci Injectivity of Modules
Bull. Korean Math. Soc.
Published online May 7, 2020
Burcu Ungor
Ankara University
Abstract : For the question ``when is $E(_RR)$ a flat left $R$-module for any ring $R$?",
in this paper, we deal with a class of modules partaking in the
hierarchy of injective and cotorsion modules, so-called Harmanci
injective modules, which turn out by the motivation of relations
among the concepts of injectivity, flatness and cotorsionness. We
give some characterizations and properties of this class of
modules. It is shown that the class of all Harmanci injective
modules is enveloping, and forms a perfect cotorsion theory with
the class of modules whose character modules are Matlis injective.
For the objective we pursue, we characterize when the injective
envelope of a ring as a module over itself is a flat module.
Keywords : Injective module, Matlis injective module, Harmanci injective module, cotorsion module, flat module, character module, envelope
MSC numbers : 16D10; 16D40; 16D50; 16E30.
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