I am a PhD student in Mathematics at the Department of Mathematics and Scientific Computing, University of Graz (Austria), working under the supervision of Prof. Alfred Geroldinger in the Algebra and Number Theory group.
My research focuses on factorization theory in rings and monoids, its connections with algebraic number theory, and the study of power monoids.
I expect to defend my thesis on June 25th 2026.
[5] A counterexample to an isomorphism problem for power monoids, Proc. Amer. Math. Soc., 2026.
[4] A characterization of transfer Krull orders in Dedekind domains with torsion class group, Canadian Mathematical Bulletin, to appear.
[3] with D. Spirito, The ramification tree and almost Dedekind domains of prescribed SP-rank, Pacific J. Math. 337 (2025), 273-295.
[2] with D. Spirito, A realization theorem for almost Dedekind domains, Communications in Algebra 54 (2026), 393-409.
[1] A characterization of half-factorial orders in algebraic number fields, Acta Arithmetica, 217 (2025), 1-17.
[2] The isomorphism problem for reduced finitary power monoids, 2026
[1] The automorphism group of reduced power monoids of finite abelian groups, 2025
On half-factorial orders in algebraic number fields, Conference on Rings and Factorizations, Graz (Austria), July 2023
On the arithmetic of orders in algebraic number fields, 9th China-Japan-Korea International Conference on Module Theory, Incheon (South Korea), August 2023
On half-factorial orders in algebraic number fields, The 25th Central European Number Theory Conference, Sopron (Hungary), August 2023
On the SP-rank of almost Dedekind domains, 9th European Congress of Mathematics, Seville (Spain), July 2024 (invited talk)
On transfer Krull orders in Dedekind domains, Advances in Commutative Ring Theory, Catania (Italy), September 2024 (invited talk)
On algebraic properties of power monoids, SAAAJ Seminar, University of Ljubljana (Slovenia), May 2025
On power monoids and their algebraic properties, Conference on Rings and Polynomials, Graz (Austria), July 2025
On power monoids and their automorphisms, Recent Trends in the Theory of Power Semigroups Workshop, HebNU School of Mathematical Sciences (China), September 2025 (invited online talk)
On isomorphisms between power monoids, Algebra and Functional Analysis Seminar, University of Ljubljana (Slovenia), December 2025 (invited talk)
Email: balint.rago@uni-graz.at