ERHARD AICHINGER
Course announcement
Universal algebra
Some basic knowlegde of classical algebra (groups, rings, fields),
as acquired in introductory first year algebra courses.
The first part of the course will follow
Chapters I and II of the book
[4][Burris and Sankappanavar, 1981].
 The elements of universal algebra: subdirect representation,
varieties and Birkhoff's HSPtheorem,
equational logic, Mal'cev conditions.
 Finite state acceptors and Kleene's Theorem on
regular languages.
 Jónsson's Theorem for congruence distributive varieties.
The second part will focus on recent research.
 Clones, polynomial and term functions of an algebra.
 Algorithmic problems in universal algebra.
[Burris and Sankappanavar, 1981]:
This book is freely available at
We will also discuss material from
[Pöschel and Kaluznin, 1979], [McKenzie et al., 1987], [Aichinger, 2010].
 Aichinger, 2010

Aichinger, E. (2010).
Constantive Mal'cev clones on finite sets are finitely related.
Proc. Amer. Math. Soc., 138(10):35013507.
 Burris and Sankappanavar, 1981

Burris, S. and Sankappanavar, H. P. (1981).
A course in universal algebra.
Springer New York Heidelberg Berlin.
 McKenzie et al., 1987

McKenzie, R. N., McNulty, G. F., and Taylor, W. F. (1987).
Algebras, lattices, varieties, Volume I.
Wadsworth & Brooks/Cole Advanced Books & Software, Monterey,
California.
 Pöschel and Kaluznin, 1979

Pöschel, R. and Kaluznin, L. A. (1979).
Funktionen und Relationenalgebren, volume 15 of Mathematische Monographien [Mathematical Monographs].
VEB Deutscher Verlag der Wissenschaften, Berlin.
Ein Kapitel der diskreten Mathematik. [A chapter in discrete
mathematics].
Students will present their solutions of the homework problems.
The lecture will start on Tuesday, March 1st, 2011,
08:30  10:00 in lecture hall HS 14.
In our first meeting on March 1st, 8:30,
practical issues such as the language of instruction
will be discussed.
The exercise class will first meet in HS 11 on March 7th, 12:45.
http://www.kusss.jku.at.
Course announcement
Universal algebra
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