Displaying similar documents to “A Generalization of Baer's Lemma”

Precovers and Goldie’s torsion theory

Ladislav Bican (2003)

Mathematica Bohemica

Similarity:

Recently, Rim and Teply , using the notion of τ -exact modules, found a necessary condition for the existence of τ -torsionfree covers with respect to a given hereditary torsion theory τ for the category R -mod of all unitary left R -modules over an associative ring R with identity. Some relations between τ -torsionfree and τ -exact covers have been investigated in . The purpose of this note is to show that if σ = ( 𝒯 σ , ℱ σ ) is Goldie’s torsion theory and ℱ σ is a precover class, then ℱ τ is a precover class...

Characterizations of incidence modules

Naseer Ullah, Hailou Yao, Qianqian Yuan, Muhammad Azam (2024)

Czechoslovak Mathematical Journal

Similarity:

Let R be an associative ring and M be a left R -module. We introduce the concept of the incidence module I ( X , M ) of a locally finite partially ordered set X over M . We study the properties of I ( X , M ) and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.

τ -supplemented modules and τ -weakly supplemented modules

Muhammet Tamer Koşan (2007)

Archivum Mathematicum

Similarity:

Given a hereditary torsion theory τ = ( 𝕋 , 𝔽 ) in Mod- R , a module M is called τ -supplemented if every submodule A of M contains a direct summand C of M with A / C τ - torsion. A submodule V of M is called τ -supplement of U in M if U + V = M and U ∩ V ≤ τ ( V ) and M is τ -weakly supplemented if every submodule of M has a τ -supplement in M . Let M be a τ -weakly supplemented module. Then M has a decomposition M = M 1 ⊕ M 2 where M 1 is a semisimple module and M 2 is a module with τ ( M 2 ) ≤ e M 2 . Also, it is shown that; any finite sum of τ -weakly...

Torsion points in families of Drinfeld modules

Dragos Ghioca, Liang-Chung Hsia (2013)

Acta Arithmetica

Similarity:

Let Φ λ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for Φ λ for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for Φ λ , then we show that for each λ ∈ K̅, a(λ) is torsion for Φ λ if and only if b(λ) is torsion for Φ λ . In the case a,b ∈ K, we prove in addition that a and b must be ̅ p -linearly dependent.