Course: Universal Algebra
 Email address of course instructor: erhard [] algebra.unilinz.ac.at
 First meeting: Tuesday, March 1st, 2011, 8:30, HS 14.
 Registration (KUSSS).
Homework problems
 Problems for March 7: 5 problems from
Chapter I, Exercises Par. 1.
 Problems for March 14:
Ch. I, Par. 2: 4,5,6.
Ch. I, Par. 3: 2,4,5.
 Problems for March 21:
Ch I, Par 3: 2 (hint: find a description of the elements in the
ideal generated by J \cup K with J,K ideals),
4 (hint: if x \not\le y, then a minimal j with
j \le x, j \not\le y, is join irreducible).
Ch I, Par 4: 5, 4 (difficult, but try to prove at least one direction).
Ch I, Par 5: 2.
 Problems for March 28:
Ch I, Par 4: 4 (=>: first produce a compact c with a_1 < c <= a_2.
Then let d := sup {x  x < c}.
Among these, find b_1, b_2.
<=: Take a such that a is not the join of
compact elements.
Show that for all c,d with c \lcover d,
d is compact.)
Ch I, Par 5: 7,8.
Ch II, Par 1: 1,2.
 Problems for April 4:
Remaining problems from March 28:
Ch I, Par 5: 8.
Ch II, Par 1: 1.
New Problems: 3 from the following 5:
Ch II, Par 3: 1.
Ch II, Par 4:1,2,3,4.
 Problems for April 11:
Remaining problems from March 28:
Ch II, Par 4:3 (find a proof not referring to Theorem II.4.4).
New problems: 4 from the following 5:
Ch II, Par 5: 2,3,7,11,12.
 Problems for May 2:
Remaining problems from April 11: II.5.11, II.5.12.
New Problems: II.6.2, II.6.3, II.6.5, II.6.6.
 Problems for May 9:
Remaining problems from May 2: II.6.2, II.6.6.
New Problems: 4 out of II.7.1, II.7.3, II.7.4, II.7.5, II.8.1, II.8.6.
 Problems for May 16:
Remaining problems from May 9: II.7.4, II.8.6.
New Problems: II.8.11, II.9.1, II.9.2.
 Problems for May 23:
Remaining problems: II.7.4 (Use (a \meet b) \circ a^* =
a^* \circ (a \meet b).
II.8.6 (Describe infinite abelian groups with
a least nontrivial subgroup).
II.9.2.
New Problems: II.8.8., II.9.5., II.10.7.
 Problems for May 30: Remaining: II.8.8., II.9.5, II.10.7.
New: II.10.1.,II.10.4.,II.10.6.
 Problems for June 20: Remaining: II.10.1.,II.10.4.
New:II.11.1., II.11.2., II.11.3.
Course material

A
Course in Universal Algebra by
Burris and
Sankappanavar.
 Notes on clone theory.
 Constantive Mal'cev clones on finite sets are finitely related
[pdf].
Since the material is copyright, please
contact me
to obtain a copy if you have no free access to PAMS.
 On the number of finite algebraic structures.
[pdf].
 Presentation of finite relatedness of Mal'cev clones
[pdf]
Webpage maintained by Erhard Aichinger