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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, 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.