Exams: Math 2/3

Sophie Frisch

Research interests: Primary: algebra, Subsidiary: number theory, topology, combinatorics, and logic.
Pet mathematical objects: commutative rings, polynomial mappings and integer-valued polynomials.

Papers and Preprints

Publication list with links

with S. Nakato and R. Rissner, Split absolutely irreducible integer-valued polynomials over discrete valuation domains, to appear in J. Algebra; preprint 2107.14276 on arxiv.

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 C. Finocchiaro and D. Windisch, Prime Ideals in Infinite Products of Commutative Rings, submitted; preprint 2009.03069 on arxiv.

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. (preprint PDF, also 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

Phone: +43(316)873-7133
Fax: +43(316)873-107133
Webpages of previous courses
TU Graz math dept web page

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?