Research interests: Primary: algebra,
Subsidiary: number theory, topology,
combinatorics, and logic.
Pet mathematical objects: commutative rings,
polynomial mappings and integer-valued
polynomials.
with V. Fadinger, S. Nakato, D. Smertnig, and D. Windisch, Primes and Absolutely or Non-Absolutely Irreducible Elements in Atomic Domains, preprint arXiv:2411.01051.
with F. Halter-Koch, P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials, to appear in M. Brešar, A. Geroldinger, B. Olberding, and D. Smertnig (eds.) Proceedings of the Conference on Rings and Factorizations in Graz 2023, Springer 2025
with C. Finocchiaro and D. Windisch, Prime Ideals in Infinite Products of Commutative Rings, Commun. Contemp. Math. 26(8) (2024), Paper No. 2350045, 24. https://doi.org/10.1142/S0219199723500451, preprint 2009.03069 on arxiv.
with V. Fadinger-Held and D. Windisch, Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations, Monatsh. Math. 202(4) (2023) 773-789, open access: https://doi.org/10.1007/s00605-023-01895-2,
with S. Nakato and R. Rissner, Split absolutely irreducible integer-valued polynomials over discrete valuation domains, J. Algebra 602 (2022) 247-277; open access: https://doi.org/10.1016/j.jalgebra.2022.03.006.
with A. Al-Maktry and H. Al-Ezeh, Polynomial functions on rings of dual numbers over residue class rings of the integers, Math. Slovaca 71 (5) 2021, 1063-1088, http://doi.org/10.1515/ms-2021-0039
with S. Nakato, A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator, Comm. Algebra 48(9) (2020), 3716-3723, open access: https://doi.org/10.1080/00927872.2020.1744618 (preprint arXiv:1912.10535)
Simultaneous interpolation and P-adic approximation by integer-valued polynomials, in A. Facchini, M. Fontana, A. Geroldinger, B. Olberding (eds.), Advances in Rings, Modules and Factorizations (proceedings of the Conference on Rings and Factorizations, Feb 19-23, 2018 at KFU Graz), pp 183-192 Springer 2020, ISBN 978-3-030-43415-1
Polynomial functions on non-commutative rings - a link between ringsets and null-ideal sets (preprint PDF), in the proceedings of the International Conference on Mathematics "recent advances in algebra, ..." at Ton Duc Thang University, Vietnam Dec. 18-20, 2018.
with S. Nakato and R. Rissner, Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields, J. Algebra 528 (2019), 231-249 (open access).
On the spectrum of rings of functions, J. Pure Appl. Algebra 222 (2018) (8), 2089-2098, (preprint arXiv:1604.04866), Link to open access on J. Pure Appl. Algebra webpage.
Polynomial functions on upper triangular matrix algebras, Monatsh. Math. 184(2) (2017) 201-215, (preprint: arXiv:1605.06027) - Link to open access on Monatsh. Math. website
Relative polynomial closure and monadically Krull monoids of integer-valued polynomials, in "Multiplicative Ideal Theory and Factorization Theory. Commutative and Non-Commutative Perspectives", S. Chapman, M. Fontana, A. Geroldinger and B. Olberding (eds.), pp 145 - 157. Springer 2016, ISBN 978-3-319-38853-3. (dvi) (ps) arXiv:1409.1111
with P.-J. Cahen, M. Fontana and S. Glaz, Open problems in commutative ring theory in ``Commutative Algebra'', M. Fontana, S. Frisch, S. Glaz (eds.), Springer 2014, ISBN: 978-1-4939-0924-7, pp 353-375.
A construction of integer-valued polynomials with prescribed sets of lengths of factorizations (PDF) - Monatsh. Math. 171 (2013) (3) 341-350 (dvi) (ps) Link to open access (doi: 10.1007/s00605-013-0508-z)
with D. Krenn, Sylow p-groups of polynomial permutations on the integers mod pn (PDF) J. Number Th. 133 (12) (2013) 4188-4199, (dvi) (ps) (doi: 10.1016/j.jnt.2013.06.002)
Integer-valued polynomials on algebras (PDF) J. Algebra 373 (2013) 414-425, (preprint pdf) (dvi) (ps) (doi: 10.1016/j.jalgebra.2012.10.003)
with L.N. Vaserstein, Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples, J. Pure Appl. Algebra 216 (1) 2012, 184-191. (dvi) (ps) (doi: 10.1016/j.jpaa.2011.06.002)
with Ch. Frei, Non-unique factorization of polynomials over residue class rings of the integers, Comm. Algebra 39(4) (2011) 1482-1490 (dvi) (ps) (doi: 10.1080/00927872.2010.549158)
Integer-valued polynomials on algebras - a survey. , Actes du CIRM 2 (2010) no 2, 27-32. (dvi) (ps)
with G. Lettl, Polynomial parametrization of the solutions of Diophantine equations of genus 0, Funct. Approx. Comment. Math. 39 (2008) (2) (Narkiewicz Volume) 205-209. (dvi) (ps) (doi: 10.7169/facm/1229696571)
Remarks on Polynomial Parametrization of Sets of Integer Points, Comm. Algebra 36 (2008) (3) 1110-1114 (abstract) (dvi) (ps) (doi: 10.1080/00927870701776938)
with L.N. Vaserstein, Parametrization of Pythagorean triples by a single triple of polynomials J. Pure Appl. Algebra 212(2008) (1) 271--274 (abstract) (dvi) (ps) (doi: 10.1016/j.jpaa.2007.05.019)
Polynomial Separation of Points
in Algebras
in: S. Chapman (ed.), Arithmetical Properties of Commutative Rings and
Modules (Chapel Hill 2013 Conf.), Chapman&Hall/CRC 2005, pp 249-254.
(abstract)
(dvi)
(ps)
(doi: 10.1201/9781420028249.ch15)
Integrally closed domains,
minimal polynomials, and null ideals of matrices.
Comm. Algebra 32(5) (2004) 2015--2017
(abstract)
(dvi)
(ps)
(doi: 10.1081/AGB-120029919)
Nullstellensatz and Skolem properties for
integer-valued polynomials
J. reine angew. Math. (Crelle) 536 (2001) 31--42
(abstract)
(dvi)
(ps)
(doi: 10.1515/crll.2001.051)
with P.-J. Cahen and J.-L. Chabert:
Interpolation domains
J. Algebra 225 (2000), 794--803.
(abstract)
(dvi)
(ps)
(doi: 10.1006/jabr.1999.8151)
Interpolation by
integer-valued polynomials
J. Algebra 211 (1999) 562--577
(abstract)
(dvi)
(ps)
(doi: 10.1006/jabr.1998.7741)
Polynomial functions on finite commutative
rings
in Advances in Commutative Ring Theory,
Proc. of Fez 1997 Conf., D.E. Dobbs et al (eds.), Dekker 1999, 323--336
(abstract)
(dvi)
(ps)
(other ps)
with M. Pasteka (Pa\v st\'eka), R. Tichy and R. Winkler:
Finitely Additive Measures on Groups and Rings
Rend. Circ. Math. Palermo (2) 48 (1999) 323--340
(abstract)
(dvi)
(ps)
(crummy
scan)
(doi: 10.1007/BF02857307)
Binomial coefficients generalized w.r.t. a
discrete valuation
Applications of Fibonacci Numbers, Proc. of Graz Conf. 1996,
G.E. Bergum et al. (eds.), Kluwer 1998, pp 133--144.
(abstract)
(ps)
(dvi)
On the minimal distance between group tables (PDF)
- Contains a counterexample to and a correction of a "theorem" of
J. Denes, Thm 4.1 on p293
of Ch.9 (by Denes and Keedwell), in "Latin Squares - New
developments (...)", J.Denes and A.D.Keedwell (eds) Elsevier 1991.
Acta. Sci. Math. (Szeged) 63 (1997) 341--351.
(abstract)
(dvi)
(ps)
(journal)
Integer-valued polynomials on Krull rings
Proc. Amer. Math. Soc. 124 (1996) 3595--3604
(abstract)
(dvi)
(ps)
(doi: 10.1090/S0002-9939-96-03442-9)
Substitution and closure of sets under
integer-valued polynomials
J. Number Theory, 56 (1996) 396--403
(abstract)
(dvi)
(ps)
(doi: 10.1090/S0002-9939-96-03442-9)
When are weak permutation polynomials strong?
Finite Fields and Appl. 1 (1995) 437--439
(abstract)
(dvi)
(ps)
(ps)
(crummy
scan)
(doi: 10.1006/ffta.1995.1034)
Some photos from the Fes Conference on Commutative Rings, 1997.
Not math related boring photos:
Windows;
Chicago Metra in a snowstorm;
blurry kingfisher and junko;
lunar eclipse;
Sophie Frisch
Institut für Analysis und Zahlentheorie (Inst. 5010)
Technische Universität Graz
Kopernikusgasse 24
8010 Graz,
Austria
I guess I do not have to point out that the wish list by "Sophie Frisch" on amazon.de was compiled by someone completely unrelated?