Course: Universal Algebra

• E-mail address of course instructor: erhard [] algebra.uni-linz.ac.at
• First meeting: Tuesday, March 1st, 2011, 8:30, HS 14.
• Registration (KUSSS).

Course description

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]

Web-page maintained by Erhard Aichinger