ERHARD AICHINGER

Course announcement
Universal algebra

Prerequisites

Some basic knowlegde of classical algebra (groups, rings, fields), as acquired in introductory first year algebra courses.

Content

The first part of the course will follow Chapters I and II of the book
[4][Burris and Sankappanavar, 1981].

1. The elements of universal algebra: subdirect representation, varieties and Birkhoff's HSP-theorem, equational logic, Mal'cev conditions.
2. Finite state acceptors and Kleene's Theorem on regular languages.
3. Jónsson's Theorem for congruence distributive varieties.

The second part will focus on recent research.

1. Clones, polynomial and term functions of an algebra.
2. Algorithmic problems in universal algebra.

Literature

[Burris and Sankappanavar, 1981]: This book is freely availabe at

http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html.

We will also discuss material from [Pöschel and Kaluznin, 1979], [McKenzie et al., 1987], [Aichinger, 2010].

Bibliography

Aichinger, 2010

Aichinger, E. (2010).
Constantive Mal'cev clones on finite sets are finitely related.
Proc. Amer. Math. Soc., 138(10):3501-3507.

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].

Exercise classes

Students will present their solutions of the homework problems.

Dates

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.

Registration

http://www.kusss.jku.at.

About this document ...

Course announcement
Universal algebra

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