Weakly projective and weakly injective modules
SK Jain, SR López-Permouth, K Oshiro… - Canadian Journal of …, 1994 - cambridge.org
A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …
Right perfect rings with the extending property on finitely generated free modules
P Dan - Osaka J. Math, 1989 - projecteuclid.org
And he has found two new classes of rings which are characterized by ideal theoretic
conditions: one is perfect rings with (*) and the other one is semiperfect rings with (*)*. In [9] …
conditions: one is perfect rings with (*) and the other one is semiperfect rings with (*)*. In [9] …
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 …
When every S-flat module is (flat) projective
D Bennis, A Bouziri - Communications in Algebra, 2024 - Taylor & Francis
Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this
paper is to study the class of commutative rings in which every S-flat module is flat (resp …
paper is to study the class of commutative rings in which every S-flat module is flat (resp …
Semiregular modules and F-semiperfect modules
W Xue - Communications in Algebra, 1995 - Taylor & Francis
Let R be a ring with Jacobson radical J (R). Following CNI, a submodule N of a left R-
module RM is said to lie over a summand of M if there exists an idempotent e E End (RM) …
module RM is said to lie over a summand of M if there exists an idempotent e E End (RM) …
Characterization of rings using quasiprojective modules. III
JS Golan - Proceedings of the American Mathematical Society, 1972 - ams.org
A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …
Max-projective modules
Y Alagöz, E Büyükaşık - Journal of Algebra and its Applications, 2021 - World Scientific
Weakening the notion of R-projectivity, a right R-module M is called max-projective provided
that each homomorphism f: M→ R/I, where I is any maximal right ideal, factors through the …
that each homomorphism f: M→ R/I, where I is any maximal right ideal, factors through the …
On weakly projective modules
SK Jain, SR López-Permouth… - Ring Theory, Proceedings …, 1992 - World Scientific
ABSTRACT A module M Is said to be weakly projective If and only If It has a projective cover
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …
[引用][C] Rings which have flat injective modules
RR Colby - Journal of algebra, 1975 - Elsevier
We shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …
paper is to characterize left and two-sided IF rings in several ways and to give some …
[引用][C] F-semi-perfect modules
G Azumaya - Journal of Algebra, 1991 - Elsevier
Let R be a ring with Jacobson radical J. Bass [1] called R semi-perfect if the factor ring R/J is
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …