The research of the Algebra and Number Theory Group at the Institute of Mathematics and Scientific Computing at the University of Graz (Austria) spans topics from (commutative and noncommutative) ring theory and module theory. We are particularly interested in the arithmetic of rings and monoids, the interaction between their arithmetic and their algebraic structure, their multiplicative ideal theory, and their factorization theory. The monoids we mainly have in mind stem from ring and module theory. For instance, we study the structure of monoids of modules in order to understand their direct-sum decompositions.
Studying factorizations of elements into irreducibles, transfer techniques allow to shift arithmetical questions in rings to problems in additive combinatorics. Thus, topics in additive combinatorics, including zero-sum problems, addition theorems, and polynomial methods, also count among our research interests.
We regularly collaborate with international colleagues from (amongst others) Canada, China, France, Italy, and the United States, and we participate in the FWF funded Doctoral Program Discrete Mathematics and the Doctoral Academy Graz.
Aqsa Bashir, MPhil
Multiplicative ideal theory, factorization theory, zero-sum theory
Laura Cossu, PhD
Commutative rings, matrix theory, factorization theory
Susan El-Deken, Visiting Professor
Matrix Theory, Factorization Theory, Additive Combinatorics
(Partially supported by the Simons Foundation, IMU-SIMONS African Fellowship Program Grant)
Alfred Geroldinger, Ao. Univ.-Prof.
Multiplicative ideal theory, factorization theory, additive combinatorics, zero-sum theory
Franz Halter-Koch, Univ.-Prof.
Algebraic number theory, multiplicative ideal theory, factorization theory, quadratic irrationals
Zahra Nazemian, PhD
Module theory, Noncommutative algebra and ring theory, Homological algebra and its application in ring theory
Andreas Reinhart, Priv.-Doz.
Commutative rings, multiplicative ideal theory, factorization theory
Gülşen Ulucak, Visiting Professor
Commutative ring, module theory and lattice theory
(supported by 2219-International Postdoctoral Research Fellowship Program of The Scientific and Technological Research Council of Turkey)
Qinghai Zhong, PhD
Additive Combinatorics and Combinatorial Factorization Theory