algebra universalis

, Volume 36, Issue 1, pp 66–80 | Cite as

Many-sorted algebras in congruence modular varieties

  • C. A. Wolf


We present several basic results on many-sorted algebras, most of them only valid in congruence modular varieties. We describe a connection between the properties of many-sorted varieties and those of varieties of one sort and give some results on functional completeness, the commutator and Abelian algebras.

1991 Mathematics subject classification

08A05 08A40 08B10 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Burris, S.,Separating sets in modular lattices with application to congruence lattices. Algebra Universalis5 (1975), 213–223.Google Scholar
  2. [2]
    Burris, S. andSankappanavar, H. P.,A course in universal algebra. Springer, New York, 1981.Google Scholar
  3. [3]
    Cohn, P. M.,Universal algebra. D. Reidel, Dordrecht, 1981.Google Scholar
  4. [4]
    Day, A. andKiss, E. W.,Frames and rings in congruence modular varieties. J. Algebra109 (1987), 479–507.Google Scholar
  5. [5]
    Ehrich, H.-D., Gogolla, M. andLipeck, U. W.,Algebraische Spezifikationen abstrakter Datentypen. Teubner, Stuttgart, 1989.Google Scholar
  6. [6]
    Ehrig, H. andMahr, B.,Fundamentals of algebraic specification 1. EATCS Monographs on Theoretical Computer Science 6, Springer, Berlin, 1985.Google Scholar
  7. [7]
    Foster, A. L. andPixley, A. F.,Semicategorial algebras I, II. Math Z.83 (1964), 147–169 and Math. Z.85 (1964), 169–184.Google Scholar
  8. [8]
    Freese, R. andMcKenzie, R.,Commutator theory for congruence modular varieties. LMS Lecture Notes Series 125, Cambridge University Press, Cambridge, 1987.Google Scholar
  9. [9]
    Gumm, H. P.,Geometrical methods in congruence modular algebras. Memoirs Amer. Math. Soc.286 (1983).Google Scholar
  10. [10]
    Hagemann, J. andHerrmann, C.,A concrete ideal multiplication of algebraic systems and its relations to congruence distributivity. Arch. Math.32 (1979), 234–245.Google Scholar
  11. [11]
    Herrmann, C.,Affine algebras in congruence modular varieties. Acta Sci. Math. Szeged41 (1979), 119–125.Google Scholar
  12. [12]
    Higgins, P. J.,Algebras with a scheme of operators. Mathematische Nachrichten27 (1963), 115–132.Google Scholar
  13. [13]
    Ihringer, T.,Allgemeine Algebra. Teubner, Stuttgart, 1993.Google Scholar
  14. [14]
    McKenzie, R., McNulty, G. F. andTaylor, W. F.,Algebras, lattices, varieties, vol. 1. Wadsworth, Belmont, Cal., 1987.Google Scholar
  15. [15]
    Meinke, K. andTucker, J. V.,Universal Algebra. In S. Abramsky, D. M. Gabbay and T. S. E. Maibaum, editors,Handbook of logic in computer science, vol. 1. Oxford University Press, Oxford, 1992, 189–411.Google Scholar
  16. [16]
    Pedicchio, M. C.,A categorical approach to commutator theory. J. Algebra177 (1995), 647–657.Google Scholar
  17. [17]
    Pöschel, R. andKaluznin, L. A.,Funktionen- und Relationenalgebren. Birkhäuser, Basel, 1979.Google Scholar
  18. [18]
    Taylor, W.,Characterizing Mal'cev conditions. Algebra Universalis3 (1973), 351–397.Google Scholar
  19. [19]
    Werner, H.,Eine Charakterisierung funktional vollständiger Algebren. Arch. Math.21 (1970), 381–385.Google Scholar
  20. [20]
    Werner, H.,Congruences on products of algebras and functionally complete algebras. Algebra Universalis4 (1974), 99–105.Google Scholar

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • C. A. Wolf
    • 1
  1. 1.Technische Hochschule DarmstadtFB MathematikDarmstadtGermany

Personalised recommendations