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Abstract
The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation to the module theoretic setting and prove that this relation is a partial order when the module is regular. Moreover, various characterizations of the minus partial order in regular modules are presented and some well-known results are also generalized.
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Acknowledgment
The authors would like to thank the referee for valuable suggestions which improved the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The work is partially supported by Slovene Research Agency, ARRS (Slovene-Turkish Grant BI-TR/17-19-004 and research core funding (No. P1-0288) and by The Scientific and Technological Research Council of Turkey, TUBITAK (Grant TUBITAK-116F435). The authors wish to thank ARRS and TUBITAK for financial support.