HOMOLOGICAL OBJECTS OF MIN-PURE EXACT SEQUENCES

Author:

ALAGÖZ Yusuf1ORCID,MORADZADEH-DEHKORDI Ali2ORCID

Affiliation:

1. SIIRT UNIVERSITY, DEPARTMENT OF MATHEMATICS, SIIRT, TURKEY

2. DEPARTMENT OF SCIENCE, SHAHREZA CAMPUS, UNIVERSITY OF ISFAHAN, IRAN

Abstract

In a recent paper, Mao has studied min-pure injective modules to investigate the existence of min-injective covers. A min-pure injective module is one that is injective relative only to min-pure exact sequences. In this paper, we study the notion of min-pure projective modules which is the projective objects of min-pure exact sequences. Various ring characterizations and examples of both classes of modules are obtained. Along this way, we give conditions which guarantee that each min-pure projective module is either injective or projective. Also, the rings whose injective objects are min-pure projective are considered. The commutative rings over which all injective modules are min-pure projective are exactly quasi-Frobenius. Finally, we are interested with the rings all of its modules are min-pure projective. We obtain that a ring R is two-sided Kothe if all right R-modules are min-pure projective. Also, a commutative ring over which all modules are min-pure projective is quasi-Frobenius serial. As consequence, over a commutative indecomposable ring with J(R)^2 = 0, it is proven that all R-modules are min-pure projective if and only if R is either a field or a quasi-Frobenius ring of composition length 2.

Funder

SCHOOL OF MATHEMATICS, INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM), TEHRAN, IRAN

Publisher

Hacettepe University

Subject

Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis

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