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.


Daniel Smertnig
Daniel Smertnig, Univ.-Prof. (Head) Noncommutative rings, factorization theory, quaternion algebras, noncommutative rational series
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Casper Barendrecht, MSc (PhD student)
Aqsa Bashir
Aqsa Bashir, MPhil (PhD student) Multiplicative ideal theory, factorization theory, zero-sum theory
Laura Cossu
Laura Cossu, PhD Commutative rings, matrix theory, factorization theory
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Victor Fadinger, Mag. (PhD student)
Alfred Geroldinger
Alfred Geroldinger, Ao. Univ.-Prof. Multiplicative ideal theory, factorization theory, additive combinatorics, zero-sum theory
Franz Halter-Koch
Franz Halter-Koch, Univ.-Prof. (retired) Algebraic number theory, multiplicative ideal theory, factorization theory, quadratic irrationals
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Florian Kainrath, Ass.-Prof.
Azeem Khadam
Azeem Khadam, PhD Commutative Algebra and (its view towards) Algebraic Geometry
Günter Lettl
Günter Lettl, Ao. Univ-Prof. (retired)
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Andreas Reinhart, Priv.-Doz. Commutative rings, multiplicative ideal theory, factorization theory
Daniel Scharler
Daniel Scharler, Dr. Factorization of polynomials over quaternion algebras and applications to kinematics

Former Members

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