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Let G be a group, R an integral domain, and V G the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero. Motivated by the Mathieu conjecture [Mathieu O., Some conjectures about invariant theory and their applications, In: Algèbre non Commutative, Groupes Quantiques et Invariants, Reims, June 26–30, 1995, Sémin. Congr., 2, Société Mathématique de France, Paris, 1997, 263–279], the Duistermaat-van der Kallen...
Let m ≥ 2 be an integer. By using m submodules of a given module, we construct a certain exact sequence, which is a well known short exact sequence when m = 2. As an application, we compute a minimal projective resolution of the Jacobson radical of a tiled order.
An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.
Let R be a ring with identity such that R⁺, the additive group of R, is torsion-free. If there is some R-module M such that and , we call R a Zassenhaus ring. Hans Zassenhaus showed in 1967 that whenever R⁺ is free of finite rank, then R is a Zassenhaus ring. We will show that if R⁺ is free of countable rank and each element of R is algebraic over ℚ, then R is a Zassenhaus ring. We will give an example showing that this restriction on R is needed. Moreover, we will show that a ring due to A....
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
The purpose of this paper is to prove the following result: Let be a -torsion free semiprime ring and let be an additive mapping, such that holds for all . In this case is left and right centralizer.
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