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Math 619
Spring 2015
Lecture: Tuesday, Thursday 3:00-4:15, in Keller 403
Instructor:
Ralph Freese
Office: 305 Keller
Phone: 956-9367
email:email me
Office hours: T-Th 4:15-5:00, F 1-2 and by appointment (or just come
to my office
and see if I'm in)
Roadmap for abelian algebras in CM varieties
Text
- Cliff Bergman, Universal Algebra, CRC Press, 2010.
Software
Books and Surveys
There are several good books in this area but many are out of print.
Fortunately many are available online.
- J. B. Nation Notes on Lattice Theory,
online at
JB's Books page.
- Burris and Sankappanavar, A Course in Universal Algebra,
out of print but available online in
pdf form.
- Denecke and Wismath, Universal Algebra and Applications in
Theoretical Computer Science, Chapman & Hall/CRC, Boca Raton, FL,
2002. ISBN: 1-58488-254-9.
- McKenzie, McNulty, Taylor, Algebras, Lattices and Varieties,
Vol. I, AMS Chelsea.
Volumes II and III will be out soon.
- J. Jezek Universal Algebra, notes on universal algebra available
here
or on Jezek's
site.
- K. Baker Class Notes on Algebras,
Six parts:
- M. Valeriote, Introduction to Universal Algebra,
Lecture notes from the First Southern African Summer School and
Workshop on Logic, Universal Algebra, and Theoretical
Computer Science, Rand Afrikaans University, Johannesburg,
December 1999.
pdf.
- B. Jonsson, Topics in Universal Algebra, in
djvu format.
- Freese and McKenzie, Commutator Theory for Congruence Modular
Varieties, available
here.
- Hobby and McKenzie, The Structure of Finite Algebras,
Comtemporary Math., AMS, Providence, RI, 1988. ISBN: 0-8218-5073-3.
This is online:
http://www.ams.org/online_bks/conm76/. We also have the
complete book here.
- M. Clasen and M. Valeriote, Tame Congruence Theory,
in Lectures on Algebraic Model Theory,
Fields Institute Monographs, volume 15, pages 67--111,
published by the American Mathematical Society, 2002.
pdf.
- K. Kearnes and E. Kiss, The Shape of Congruence Lattices,
pdf.
- R. Willard, An overview of modern universal algebra,
pp. 197-220 in Logic Colloquium 2004, eds. A. Andretta, K. Kearnes
and D. Zambella, Lecture Notes in Logic,
vol. 29, Cambridge U. Press, 2008.
pdf.
- R. Freese and O. Garcia, Universal Algebra and Lattice Theory,
1982 Puebla Meeting, in
djvu format.
Articles and Notes
- J. Berman, The structure of free algebras,
in Structural Theory of Automata, Semigroups, and Universal Algebra,
NATO Sci. Ser. II Math. Phys. Chem., 207(2005), 47-76.
pdf.
- G. Birkhoff, On the structure of abstract algebras,
Proc. Cmabridge Phil. Soc., 31(1935), 433-454.
pdf.
- R. Freese, Computing congruences efficiently,
Algebra Universalis, 59(2008), 337-343.
pdf.
- R. Freese, Notes on the Birkhoff Construction,
pdf.
- R. Freese and M. Valeriote, On the complexity of some Maltsev
conditions, Internation J. Algebra and Computation, to appear.
pdf.
- P. P. Palfy and P. Pudlak, Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups , Algebra Universalis,
11 (1980), 22-27.
pdf.
- P. P. Palfy, Unary polynomials in algebras, I, Algebra Universalis,
18 (1984), 262-273.
pdf.
- P. Pudlak and J. Tuma, Every finite lattice can be embedded in a finite partition lattice, Algebra Universalis,
10 (1980), 74-95.
pdf.
- W. Lampe, Notes on G-sets.
pdf.
- R. Freese, Notes on concrete representations.
pdf.
- R. Freese, Notes on centrality relations, term conditions, and commutators.
pdf.
- J. Jezek,
Jarda Jezek's papers and books.
- T. Holmes, Slides for his talk:
Survey on permutohedra and associahedra,
pdf.
- Matt, et al.,
On Maltsev Conditions associated with omitting certain
types of local structures,
pdf.
- R. Freese
A note on congruence join semidistributivity,
pdf.
Actually this will be included in the above paper.
- R. Freese
Robustness of congruence join semidistributivity.
pdf.
- T. Dent, K. Kearnes, A. Szendrei,
An easy test for congruence modularity.
pdf.
- R. Freese,
Notes on n-permutability and semidistributivity.
notes,
talk.
- G. McNulty,
Undecidable properties of finite
sets of equations
, J. Symbolic Logic, 41 (1976), 589--604.
pdf.
- G. Hutchinson and G. Czedli,
A test for identities satisfied in lattices of submodules
, Algebra Universalis, 8 (1978), 269--309.
pdf.
- J. Hagemann and A. Mitschke,
On n-permutable congruences
, Algebra Universalis, 3 (1973), 8--12.
pdf.
Journals
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