Reduced rank in
JA Beachy, M Medina-Bárcenas - arXiv preprint arXiv:2201.07196, 2022 - arxiv.org
Using the concept of prime submodule introduced by Raggi et. al. we extend the notion of
reduced rank to the module-theoretic context. We study the quotient category of $\sigma [M] …
reduced rank to the module-theoretic context. We study the quotient category of $\sigma [M] …
On the nilpotence of the prime radical in module categories
C Arellano, J Castro, J Ríos - Algebra and discrete mathematics, 2021 - dspace.nbuv.gov.ua
For M∈ R-Mod and τ a hereditary torsion theory on the category σ [M] we use the concept of
prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure …
prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure …
The Torsion Theory Generated by M-Small Modules
AÇ Özcan, A Harmanci - Algebra Colloquium, 2003 - Springer
Let M be a right R-module,\cal M the class of all M-small modules, and P a projective cover
of M in σ M. We consider the torsion theories\cal M=(\cal T _\cal M,\cal F _\cal M),\tau_V=(\cal …
of M in σ M. We consider the torsion theories\cal M=(\cal T _\cal M,\cal F _\cal M),\tau_V=(\cal …
Isomorphisms between injective modules
MF Hamid - arXiv preprint arXiv:2407.19038, 2024 - arxiv.org
Suppose that $(\mathcal {F},\mathcal {M}) $ is an injective structure of $ R $-Mod such that
the class $\mathcal {F} $ is closed for direct limits, then two modules in $\mathcal {M} $ are …
the class $\mathcal {F} $ is closed for direct limits, then two modules in $\mathcal {M} $ are …
Extending modules relative to a torsion theory
S Doğruöz - Czechoslovak Mathematical Journal, 2008 - Springer
An R-module M is said to be an extending module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of a type 2 τ-extending …
summand. In this paper we introduce and investigate the concept of a type 2 τ-extending …
[PDF][PDF] Ranks of modules relative to a torsion theory
S Asgari, A Haghany - Bulletin of the Iranian Mathematical …, 2011 - bims.iranjournals.ir
Relative to a hereditary torsion theory $ tau $ we introduce a dimension for a module $ M $,
called {em $ tau $-rank of} $ M $, which coincides with the reduced rank of $ M $ whenever …
called {em $ tau $-rank of} $ M $, which coincides with the reduced rank of $ M $ whenever …
Rickart Modules Relative to Goldie Torsion Theory
Let $ R $ be an arbitrary ring with identity and $ M $ a right $ R $-module with $ S= $ End $
_R (M) $. Let $ Z_2 (M) $ be the second singular submodule of $ M $. In this paper, we …
_R (M) $. Let $ Z_2 (M) $ be the second singular submodule of $ M $. In this paper, we …
The nilpotency of the prime radical of a Goldie module
JA Beachy, M Medina-Bárcenas - arXiv preprint arXiv:2109.14043, 2021 - arxiv.org
With the notion of prime submodule defined by F. Raggi et. al. we prove that the intersection
of all prime submodules of a Goldie module $ M $, is a nilpotent submodule provided that …
of all prime submodules of a Goldie module $ M $, is a nilpotent submodule provided that …
[PDF][PDF] On τ-injective hulls of modules
S Crivei - Publ. Math. Debrecen, 2002 - scholar.archive.org
Let τ be a hereditary torsion theory on the category R-mod of left modules over an
associative unitary ring R. We will study the τ-injective hull of certain modules, giving an …
associative unitary ring R. We will study the τ-injective hull of certain modules, giving an …
Quasi-injective modules and stable torsion classes
E Armendariz - Pacific Journal of Mathematics, 1969 - msp.org
In this note we examine the 𝒯-torsion submodule of quasi-injective R-modules, R a ring with
unit, where 𝒯 is a torsion class in the sense of SE Dickson. We show that for a stable torsion …
unit, where 𝒯 is a torsion class in the sense of SE Dickson. We show that for a stable torsion …