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.