4,391 research outputs found
Wheeled props in algebra, geometry and quantization
These are expanded notes of author's talk at the ECM 2008 attempting to give
an elementary introduction into the main ideas of the theory of wheeled props
for beginners, and also a survey of its most recent major applications (ranging
from algebra and geometry to deformation theory and Batalin-Vilkovisky
quantization) which might be of interest to experts.Comment: The Proceedings versio
Semiring and semimodule issues in MV-algebras
In this paper we propose a semiring-theoretic approach to MV-algebras based
on the connection between such algebras and idempotent semirings - such an
approach naturally imposing the introduction and study of a suitable
corresponding class of semimodules, called MV-semimodules.
We present several results addressed toward a semiring theory for
MV-algebras. In particular we show a representation of MV-algebras as a
subsemiring of the endomorphism semiring of a semilattice, the construction of
the Grothendieck group of a semiring and its functorial nature, and the effect
of Mundici categorical equivalence between MV-algebras and lattice-ordered
Abelian groups with a distinguished strong order unit upon the relationship
between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of
Section
Good Reduction of Good Filtrations at Places
We consider filtered or graded algebras over a field . Assume that
there is a discrete valuation of with its maximal ideal and
its residue field. Let be -order such that
and the
-reduction of at the place . Using the filtration
of induced by we shall prove that for certain algebras their
properties are related to .Comment: 17 page
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