18,471 research outputs found
Integral closure of rings of integer-valued polynomials on algebras
Let be an integrally closed domain with quotient field . Let be a
torsion-free -algebra that is finitely generated as a -module. For every
in we consider its minimal polynomial , i.e. the
monic polynomial of least degree such that . The ring consists of polynomials in that send elements of back to
under evaluation. If has finite residue rings, we show that the
integral closure of is the ring of polynomials in which
map the roots in an algebraic closure of of all the , ,
into elements that are integral over . The result is obtained by identifying
with a -subalgebra of the matrix algebra for some and then
considering polynomials which map a matrix to a matrix integral over . We
also obtain information about polynomially dense subsets of these rings of
polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix,
integral closure, pullback, polynomially dense set. accepted for publication
in the volume "Commutative rings, integer-valued polynomials and polynomial
functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201
Polynomial functions on non-commutative rings - a link between ringsets and null-ideal sets
Regarding polynomial functions on a subset of a non-commutative ring ,
that is, functions induced by polynomials in (whose variable commutes
with the coefficients), we show connections between, on one hand, sets such
that the integer-valued polynomials on form a ring, and, on the other hand,
sets such that the set of polynomials in that are zero on is an
ideal of .Comment: 9 pages, conference paper for "advances in algebra ..." at Ton Duc
Thang University, Vietnam, Dec 18-20, 201
Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras
The present text surveys some relevant situations and results where basic
Module Theory interacts with computational aspects of operator algebras. We
tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be
published in Lecture Notes in Computer Scienc
Sylow -groups of polynomial permutations on the integers mod
We describe the Sylow -groups of the group of polynomial permutations of
the integers mod
On Linear Difference Equations over Rings and Modules
In this note we develop a coalgebraic approach to the study of solutions of
linear difference equations over modules and rings. Some known results about
linearly recursive sequences over base fields are generalized to linearly
(bi)recursive (bi)sequences of modules over arbitrary commutative ground rings.Comment: 21 pages, to appear in IJMM
- …