Results 41 to 50 of about 52,756 (165)
Fuchs' problem for indecomposable abelian groups
, 2015 More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the group of units of a commutative ring. Though progress has been made, the question remains open.
Chebolu, Sunil K., Lockridge, Keir
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Integral closure of rings of integer-valued polynomials on algebras
, 2014 Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e.
G. Peruginelli +10 more
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Specialization and Integral Closure
, 2014 We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal.
Hong, J., Ulrich, B.
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Torsion-free, divisible, and Mittag-Leffler modules [PDF]
, 2013 We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of absolutely pure modules. A final goal is to describe the K-Mittag-Leffler abelian groups as those that are, modulo their torsion part, aleph_1-free, Cor.6.12.
Philipp Rothmaler, To Leonell
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Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free
, 2011 Let (R,m) be a local ring and U_R=Spec(R) -{m} be the punctured spectrum of R. Gabber conjectured that if R is a complete intersection of dimension 3, then the abelian group Pic(U_R) is torsion-free.
Auslander +7 more
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Torsion-Free Modules over Reduced Witt Rings
Journal of Algebra, 2000 For a ring-order \(R\), \textit{R. Wiegand} and \textit{R. Guralnick} [Lect. Notes Pure Appl. Math. 189, 333-347 (1997; Zbl 0884.13004)] defined the genus class group Genus(\(M\)) of a torsion-free, finitely generated \(R\)-module \(M\). The goal of the paper under review is to show that some of these results also hold for the reduced Witt rings of ...
openaire +1 more source
Characterizations of Commutativity of Prime Ring with Involution by Generalized Derivations
MathematicsIn the paper, we investigate the commutativity of a two-torsion free prime ring R provided with generalized derivations, and some well-known results that characterize the commutativity of prime rings through generalized derivations have been generalized.
Mingxing Sui, Quanyuan Chen
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International Journal of Photoenergy, 2010 This study aimed to design a new series of compounds consisting of a porphyrin macrocycle linked to a perylene unit via a thiophenic bridge. The structural and electronic properties of the molecules, and the effects of mono- and di-substituents R on C3 ...
Tatiya Chokbunpiam +3 more
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Rigid abelian groups and the probabilistic method
, 2011 The construction of torsion-free abelian groups with prescribed endomorphism rings starting with Corner's seminal work is a well-studied subject in the theory of abelian groups.
Braun, Gábor, Pokutta, Sebastian
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On Finite-Dimensional Torsion-Free Modules and Rings [PDF]
Proceedings of the American Mathematical Society, 1970 1. This note is concerned primarily with a study of modules having zero singular submodule, called torsion-free modules, over finitedimensional rings. In some of our results we do not require that the ring be finite-dimensional but only that direct sums of torsion-free injective modules be injective, a property shown by Mark Teply to be equivalent to ...
openaire +1 more source