Unique prime factorization in a partial semigroup of matrix-polynomials

Michael Kaltenbäck; Harald Woracek

Discussiones Mathematicae - General Algebra and Applications (2006)

  • Volume: 26, Issue: 1, page 21-43
  • ISSN: 1509-9415

Abstract

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We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.

How to cite

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Michael Kaltenbäck, and Harald Woracek. "Unique prime factorization in a partial semigroup of matrix-polynomials." Discussiones Mathematicae - General Algebra and Applications 26.1 (2006): 21-43. <http://eudml.org/doc/276846>.

@article{MichaelKaltenbäck2006,
abstract = {We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.},
author = {Michael Kaltenbäck, Harald Woracek},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {partial semigroup; unique prime factorization; partial semigroups; unique prime factorizations; matrix-polynomials},
language = {eng},
number = {1},
pages = {21-43},
title = {Unique prime factorization in a partial semigroup of matrix-polynomials},
url = {http://eudml.org/doc/276846},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Michael Kaltenbäck
AU - Harald Woracek
TI - Unique prime factorization in a partial semigroup of matrix-polynomials
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2006
VL - 26
IS - 1
SP - 21
EP - 43
AB - We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.
LA - eng
KW - partial semigroup; unique prime factorization; partial semigroups; unique prime factorizations; matrix-polynomials
UR - http://eudml.org/doc/276846
ER -

References

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  1. [1] L. de Branges, Hilbert spaces of entire functions Prentice-Hall, London 1968. Zbl0157.43301
  2. [2] D. Alpay, Ya. Azizov, A. Dijksma and H. Langer, The Schur algorithm for generalized Schur functions III: J-unitary matrix polynomials on the circle, Linear Algebra Appl. 369 (2003), 113-144. Zbl1068.47020
  3. [3] D. Alpay, A. Dijksma and H. Langer, Factorization of J-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions, Linear Algebra Appl. 387 (2004), 313-342. Zbl1073.47507
  4. [4] M. Kaltenbäck and H. Woracek, Pontryagin spaces of entire functions I, Integral Equations Operator Theory 33 (1999), 34-97. Zbl0928.46011
  5. [5] M. Kaltenbäck and H. Woracek, Pontryagin spaces of entire functions II, Integral Equations Operator Theory 33 (1999), 305-380. Zbl0928.46012
  6. [6] M. Kaltenbäck and H. Woracek, Pontryagin spaces of entire functions III, Acta Sci. Math. (Szeged) 69 (2003), 241-310. Zbl1027.46024

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