Harmanci injectivity of modules
Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 973-990
https://doi.org/10.4134/BKMS.b190666
Published online July 31, 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 : Primary 16D10, 16D40, 16D50, 16E30
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