Research Output
Articles
Publication Date: 2025
Journal of Algebra and its Applications (17936829)
In this paper, we continue to study weakly uniserial modules and rings. A module is called weakly uniserial if its submodules are comparable regarding embedding. Also, a right weakly uniserial ring is a ring which is weakly uniserial as a right module over itself. In addition to providing more properties of these modules, we introduce and investigate weakly serial modules (which are a direct sum of weakly uniserial modules). A right weakly serial ring is a ring which is weakly serial as a right module over itself. It is shown that over a right Artinian local ring R, every (2-generated) right R-module with a semiprime annihilator is weakly uniserial. The converse is true when R is a commutative Noetherian ring. We prove that an injective Z-module is weakly uniserial if and only if it is isomorphic to Zp∞, for some prime number p. In a weakly serial module we show that every its nonzero submodule contains a weakly uniserial submodule and every its fully invariant submodule is weakly serial. Also, it is shown that a right duo right self-injective ring is right weakly serial if and only if every projective right module is (weakly) serial. © 2026 World Scientific Publishing Company.
Publication Date: 2024
Hacettepe Journal of Mathematics and Statistics (2651477X)53(2)pp. 342-355
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 consid-ered. 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 Köthe 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. © 2024, Hacettepe University. All rights reserved.
Publication Date: 2024
Rendiconti del Circolo Matematico di Palermo (0009725X)73(8)pp. 3175-3193
Given modules M and A, M is said to be A-RD-subinjective if for every RD-extension B of A, every f∈Hom(A,M) extends to Hom(B,M). For a module M, the RD-subinjectivity domain of M is defined to be the collection of all modules A such that M is A-RD-subinjective. We investigate basic properties of RD-subinjectivity domains and provide characterizations for various types of rings and modules including p-injective modules, RD-coflat modules, von Neumann regular rings, RD-rings, Köthe rings, right Noetherian rings, and quasi-Frobenius rings in terms of RD-subinjectivity domains. Finally, we study the properties of RD-indigent modules and consider the structure of rings over which every (resp. simple) right module is RD-injective or RD-indigent. © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2024.
