The Simple Modules of Certain Generalized Crossed Products
V. V. Bavula,F. Van Oystaeyen +1 more
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In this paper, the authors consider a Dedekind domain and a Z-graded ring R = ;⊕ i ∈ Z R i withR0 = D and eachRi = Dvibeing a free D-module of rank 1.About:
This article is published in Journal of Algebra.The article was published on 1997-08-15 and is currently open access. It has received 49 citations till now. The article focuses on the topics: Simple module & Ring (mathematics).read more
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The algebra of integro-differential operators on an affine line and its modules
TL;DR: The Strong Compact-Fredholm alternative for the Weyl algebra is proved in this paper for the algebra I 1 = K ∈ x, d d x, ∫ 〉 of polynomial integro-differential operators over a field K of characteristic zero, and a classification of simple modules is given.
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Down–Up Algebras and Their Representations
TL;DR: Benkart and Roby as mentioned in this paper proved that the down-up algebras are hyperbolic rings, and studied their representations via their left spectrum as defined in [A. L. Rosenberg, 1995, “Non-commutative Algebraic Geometry and Representations of Quantized Algebraas,” Kluwer Academic, Dordrecht].
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The algebra of integro-differential operators on an affine line and its modules
TL;DR: For the algebra of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given in this paper, where it is shown that the centralizer of a non-scalar integrodifferential operator can be a noncommutative, non-Noetherian, nonfinitely generated algebra which is not a domain.
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Simple modules of the Witten–Woronowicz algebra
V. V. Bavula,F. Van Oystaeyen +1 more
TL;DR: In this article, it was shown that Witten's second deformation and Woronowicz's deformation are isomorphic algebras, up to irreducible elements of certain noncommutative Euclidean rings.
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Simple Holonomic Modules over the Second Weyl Algebra A2
V. V. Bavula,F. Van Oystaeyen +1 more
TL;DR: For simple generalized Weyl algebras Λ of Gelfand-Kirillov dimension 4, a class including the second Weyl algebra A 2, some simple factor algesbras of the universal enveloping algebra of the Lie algebra sl(2)× sl (2) and of U q sl ( 2)× U q s (2), etc., the simple holonomic Λ -modules are classified up to pairs of irreducible elements of certain noncommutative Euclidean ring as discussed by the authors.
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The Theory of Rings
TL;DR: In this paper, the authors considered the theory of rings in which both maximal and minimal conditions hold for ideals, except in the last chapter, where rings of the type of a maximal order in an algebra are considered.
Theory of rings
TL;DR: In this paper, the authors considered the theory of rings in which both maximal and minimal conditions hold for ideals, except in the last chapter, where rings of the type of a maximal order in an algebra are considered.
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Sur les algèbres de Weyl
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.emath.org/ conditions) are defined, i.e., the copie ou impression of a fichier do not contenir the présente mention de copyright.
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The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
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A Class of Algebras Similar to the Enveloping Algebra of sl(2)
TL;DR: In this article, the enveloping algebra of sl(2, C) was studied for different f, and it was shown how they are similar to (and different from) U(sl(2)), the envelope algebra for sl(3, C).