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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


  • Cliff Bergman, Universal Algebra, CRC Press, 2010.


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, also out of print but the first two chapters have been typset by Kate Owens. Vol. II is being written. Here is Chapter 10 on Maltsev conditions.

  • 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.