Absolutely pure covers
K Pinzon - Communications in Algebra®, 2008 - Taylor & Francis
Absolutely pure modules act in ways similar to injective modules. There are conditions on a
ring which guarantee that the class of injective modules will be covering. In this article, we …
ring which guarantee that the class of injective modules will be covering. In this article, we …
Nilpotent-invariant modules and rings
Automorphism-invariant modules, due to Lee and Zhou, generalize the notion of quasi-
injective modules. A module which is invariant under automorphisms of its injective hull is …
injective modules. A module which is invariant under automorphisms of its injective hull is …
On essential extensions of direct sums of either injective or projective modules
For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum
of injective right R-modules is injective, and R is right Noetherian if and only if every …
of injective right R-modules is injective, and R is right Noetherian if and only if every …
Rings over which flat covers of finitely generated modules are projective
In Bican et al., it is proved that all modules over an arbitrary ring have flat covers. In this
article, we shall study rings over which flat covers of finitely generated modules are …
article, we shall study rings over which flat covers of finitely generated modules are …
Rings related to mininjective and min-flat modules
L Mao - Communications in Algebra, 2009 - Taylor & Francis
R is called a left PS (resp. left min-coherent, left universally mininjective) ring if every simple
left ideal is projective (resp. finitely presented, a direct summand of R). We first investigate …
left ideal is projective (resp. finitely presented, a direct summand of R). We first investigate …
Homological properties relative to injectively resolving subcategories
Z Gao - Canadian Mathematical Bulletin, 2015 - cambridge.org
Let E be an injectively resolving subcategory of le R-modules. A le R-module M (resp. right
R-module N) is called E-injective (resp. E-at) if ExtR (G, M)=(resp. TorR (N, G)=) for any G∈ …
R-module N) is called E-injective (resp. E-at) if ExtR (G, M)=(resp. TorR (N, G)=) for any G∈ …
[PDF][PDF] Small principally quasi-injective modules
S Wongwai - Int. J. Contemp. Math. Sciences, 2011 - m-hikari.com
Let M be a right R-module. A right R-module N is called small principally M-injective (briefly,
SP-M-injective) if, every R-homomorphism from a small and principal submodule of M to N …
SP-M-injective) if, every R-homomorphism from a small and principal submodule of M to N …
Absolutely s-Pure Modules and Neat-Flat Modules
E Büyükaşık, Y Durğun - Communications in Algebra, 2015 - Taylor & Francis
Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective
hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R …
hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R …
Relative FI-injective and FI-flat modules
L Duan, B Ouyang - Indian Journal of Pure and Applied Mathematics, 2011 - Springer
Let R be a ring, na fixed nonnegative integer and FP n (F n) the class of all left (right) R-
modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module …
modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module …
Direct injective modules
C Zhizhong - Acta Mathematica Sinica, 1993 - Springer
Throughout this paper R will denote a ring with idenity element and M a unitary right module
over R. An R-module M is said to be direct injective if and only if given direct summand N of …
over R. An R-module M is said to be direct injective if and only if given direct summand N of …