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Products of small modules

Peter Kálnai, Jan Žemlička (2014)

Commentationes Mathematicae Universitatis Carolinae

Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.

QTAG torsionfree modules

Ladislav Bican, Blas Torrecillas (1992)

Commentationes Mathematicae Universitatis Carolinae

The structure theory of abelian p -groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated p -group is a direct sum of cyclics. Given a hereditary torsion theory on the category R -Mod of unitary left R -modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This...

Quantization of canonical cones of algebraic curves

Benjamin Enriquez, Alexander Odesskii (2002)

Annales de l’institut Fourier

We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve C , based on the theory of formal pseudodifferential operators. When C is a complex curve with Poincaré uniformization, we propose another, equivalent construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a presentation of the quantum algebra when C is a rational curve, and discuss the problem of constructing algebraically “differential liftings”.

Quantum sections and Gauge algebras.

Lieven Le Bruyn, Freddy van Oystaeyen (1992)

Publicacions Matemàtiques

Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...

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