Orderings and preorderings on modules
Abstract
The purpose of this paper is to investigate some relevant properties of semireal modules. By introducing the notion of preorderings on modules over commutative rings, we discuss the interplay between semireality, preorderings and orderings on modules. In particular, we obtain that an R−module M is semireal if and only if M possesses a preordering. We also give some necessary and sufficient conditions for a preordering to be an ordering on modules.
Copyright © 2014 Dongming Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. Huang, Orderings and preorderings on modules, J. Math. Comput. Sci. 4 (2014), 574–586.
BibTeX
@article{Huang2014,
author = {Huang, Dongming},
title = {Orderings and preorderings on modules},
journal = {J. Math. Comput. Sci.},
volume = {4},
year = {2014},
pages = {574--586},
doi = {}
}