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We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let be a domain containing a field of characteristic zero. We prove that, when is a one-dimensional unique factorization domain, the image of any locally nilpotent -derivation of the bivariate polynomial algebra is a Mathieu-Zhao subspace. Moreover, we prove that, when is a Dedekind domain, the image of a locally nilpotent -derivation of with some additional conditions...
We describe all those indecomposable primarily comultiplication modules with finite-dimensional top over pullback of two Dedekind domains. We extend the definition and results given by R. Ebrahimi Atani and S. Ebrahimi Atani [Algebra Discrete Math. 2009] to a more general primarily comultiplication modules case.
Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.
I. S. Cohen proved that any commutative local noetherian ring R that is J(R)-adic complete admits a coefficient subring. Analogous to the concept of a coefficient subring is the concept of an inertial subring of an algebra A over a commutative ring K. In case K is a Hensel ring and the module is finitely generated, under some additional conditions, as proved by Azumaya, A admits an inertial subring. In this paper the question of existence of an inertial subring in a locally finite algebra is discussed....
We study whether the projective and injective properties of left -modules can be implied to the special kind of left -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.
In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots. These...
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