Die Struktur einer Klasse linear kompakter Ringe
Die Struktur von projektiven Moduln.
Die Translationshülle und wesentliche Erweiterungen eines zyklischen Ringes.
Die Vektorraumkategorie zu einem unzerlegbaren projektiven Modul einer tubularen Algebra.
Die Zentren hereditärer Ringe.
Differential calculus on almost commutative algebras and applications to the quantum hyperplane
In this paper we introduce a new class of differential graded algebras named DG -algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a -algebra. Then we introduce linear connections on a -bimodule over a -algebra and extend these connections to the space of forms from to . We apply these notions to the quantum hyperplane.
Differential equations and maximal ideals on the Weyl algebra
Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two
Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth.
Differentially trivial left Noetherian rings
We characterize left Noetherian rings which have only trivial derivations.
Differentially trivial Noetherian semiperfect rings.
Differentiation and splitting for lattices over orders
We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace u by a more...
Différentielles non commutatives et théorie de Galois différentielle ou aux différences
Dimension homologique de modules simples
Dimension in algebraic frames, II: Applications to frames of ideals in
This paper continues the investigation into Krull-style dimensions in algebraic frames. Let be an algebraic frame. is the supremum of the lengths of sequences of (proper) prime elements of . Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of in terms of the dimensions of certain boundary quotients of . This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are not necessarily...
Dimension injective des produits croisés.
Dimensions globales des extensions de Ore et des algèbres de Weyl
Ding projective and Ding injective modules over trivial ring extensions
Let be a trivial extension of a ring by an --bimodule such that , , and have finite flat dimensions. We prove that is a Ding projective left -module if and only if the sequence is exact and is a Ding projective left -module. Analogously, we explicitly describe Ding injective -modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.
Diophantische Gleichungen und die universelle Eigenschaft Finslerscher Zahlen.
Direct decompositions and basic subgroups in commutative group rings
An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of abelian groups over a commutative unitary ring are established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect published in Czechoslovak Math. J. (2006).
Direct finiteness of group rings - a simple proof of the Kaplansky's conjecture for finite groups