Algebra

Algebra research group is mainly interested in semigroup theory, universal algebra, and category theory, but also some problems in lattice theory and ring theory.

Research Group staff

• Professor Valdis Laan (Head of Research Group)
• Professor Emeritus Kalle Kaarli
• Lecturer Lauri Tart
• Lecturer Alvin Lepik
• Research Fellow Ülo Reimaa
• Research Fellow Nasir Sohail
• Research Fellow Kristo Väljako
• MSc student Marilyn Kutti
• MSc student Heleen Saarse
• MSc student Urmas Luhaäär

Topics:

• Morita theory of semigroups;
• Morita theory of nonunital rings;
• structure theory of semigroups;
• acts over semigroups;
• tolerances on complete lattices;
• completions of ordered algebraic structures;
• categorical equivalence of universal algebras;
• structures in higher categories;
• categorical algebra.

Research Group projects

Current projects

• PRG1204 Morita theory of semigroups and other structures
• PUTJD948 Lax monoidal structures and problems in a semi-abelian setting

Main past projects

• ETF8394 Categorical equivalence problems in algebra (01.2010-12.2013)
• PUT1519 Morita equivalence of semigroups (01.2017-12.2020)
• Exchange program between Estonian and Hungarian Academies of Sciences
• Project „Restriction semigroups: structure and interaction with order, topology, and actions“ in collaboration with Ganna Kudryavtseva from Slovenia
• PUTJD948 Lax monoidal structures and problems in a semi-abelian setting (1.07.2020−30.06.2022)

Theodor Molien (1861-1941), a prominent algebraist, began his mathematical career in Tartu.
The algebra research group of the University of Tartu started in 1955 when Jaak Hion started working here. Over time, Vladimir Fleischer, Uno Kaljulaid, Mati Kilp, Vladimir Kuchmei, Uve Nummert and Raul Roomeldi have belonged to the group.

Seminar on Algebra
In seminar talks, we consider mainly the newest scientific results of the algebraists and graduate students of the University of Tartu about Morita equivalence of semigroups and rings. The talks will be delivered both by faculty members and students.