Integer-valued polynomials on algebras: a survey

Sophie Frisch[1]

  • [1] Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 27-32
  • ISSN: 2105-0597

Abstract

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We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.

How to cite

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Frisch, Sophie. "Integer-valued polynomials on algebras: a survey." Actes des rencontres du CIRM 2.2 (2010): 27-32. <http://eudml.org/doc/196287>.

@article{Frisch2010,
abstract = {We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.},
affiliation = {Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria},
author = {Frisch, Sophie},
journal = {Actes des rencontres du CIRM},
keywords = {Integer-valued polynomials; matrices; quaternions; group rings; Prüfer domains},
language = {eng},
number = {2},
pages = {27-32},
publisher = {CIRM},
title = {Integer-valued polynomials on algebras: a survey},
url = {http://eudml.org/doc/196287},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Frisch, Sophie
TI - Integer-valued polynomials on algebras: a survey
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 27
EP - 32
AB - We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.
LA - eng
KW - Integer-valued polynomials; matrices; quaternions; group rings; Prüfer domains
UR - http://eudml.org/doc/196287
ER -

References

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  1. P.-J. Cahen and J.-L. Chabert, Integer-Valued Polynomials, Math. Surveys and Monographs 48, Amer. Math. Soc., Povidence, R.I., 1997. Zbl0884.13010MR1421321
  2. S. Frisch, Polynomial separation of points in algebras, in Arithmetical Properties of Commutative Rings and Monoids, 253–259, Lect. Notes Pure Appl. Math. 241, Chapman & Hall, Boca Raton, 2005. Zbl1092.13027MR2140698
  3. S. Frisch, Integer-valued polynomials in algebra, preprint. Zbl1273.13037
  4. F. Halter-Koch and W. Narkiewicz, Commutative rings and binomial coefficients, Monatsh. Math.114 (1992), 107–110. Zbl0764.12002MR1191815
  5. K. A. Loper, A generalization of integer-valued polynomial rings, preprint. Zbl0896.13015
  6. N. Werner, Integer-valued polynomials over quaternions rings, J. Algebra324 (2010), 1754–1769. Zbl1219.16027MR2673759
  7. N. Werner, Integer-valued polynomials over matrix rings, Comm. Algebra, to appear. 

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