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Filtered Products of Copies of Injective Modules

Axioms
We study the transfer of injectivity to filtered products of copies of an injective module. This leads to the introduction of a generalized Noetherian condition, the so-called (ℵ,M)-Noetherian rings. We prove that M is F-injective for every filter F with
Driss Bennis +3 more
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Jordan left derivations in infinite matrix rings

Demonstratio Mathematica
Let RR be a unital associative ring. Our motivation is to prove that left derivations in column finite matrix rings over RR are equal to zero and demonstrate that a left derivation d:T→Td:{\mathcal{T}}\to {\mathcal{T}} in the infinite upper triangular ...
Zhang Daochang, Ma Leiming, Hu Jianping, Sun Chaochao +3 more
doaj +1 more source

Inert Module Extensions, Multiplicatively Closed Subsets Conserving Cyclic Submodules and Factorization in Modules

پژوهش‌های ریاضی, 2019
Introduction Suppose that is a commutative ring with identity, is a unitary -module and is a multiplicatively closed subset of . Factorization theory in commutative rings, which has a long history, still gets the attention of many researchers ...
Ashkan Nikseresht
doaj

On the commutativity of torsion free rings [PDF]

Bulletin of the Australian Mathematical Society, 1984
If R is (n(n−1)/2)-torsion free ring with 1 and satisfies the identity (xy)n = xnyn, then R is commutative provided that n = 4k.
openaire +1 more source

Cubo, 2010
In this paper we prove the following result. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X, and let be a standard operator algebra. Suppose is a linear mapping satisfying the relation .
Irena Kosi-Ulbl, Joso Vukman
doaj

Absolutely torsion-free rings [PDF]