Bulletin of the American Mathematical Society

Review: Mario Petrich, Categories of algebraic systems, and Jonathan D. H. Smith, Mal′cev varieties

G. Grätzer

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Source
Bull. Amer. Math. Soc., Volume 84, Number 6 (1978), 1339-1344.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183541471

Citation

Grätzer, G. Review: Mario Petrich, Categories of algebraic systems , and Jonathan D. H. Smith, Mal′cev varieties. Bull. Amer. Math. Soc. 84 (1978), no. 6, 1339--1344. https://projecteuclid.org/euclid.bams/1183541471


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References

  • 1. B. Banaschewski and E. Nelson, Equational compactness in equational classes of algebras, Algebra Universalis 2 (1972), 152-165.
  • 2. S. Eilenberg and S. Mac Lane, Group extensions and homology, Ann. of Math. (2) 43 (1942), 757-831.
  • 3. S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294.
  • 4. P. Freyd, Abelian categories, An introduction to the theory of functors, Harper & Row, New York, 1964.
  • 5. G. Grätzer, General lattice theory, Academic Press, New York; Birkhäuser Verlag, Basel; Akademie Verlag, Berlin, 1978.
  • 6. G. Grätzer, Universal algebra, 2nd expanded ed., Springer-Verlag, New York, 1978.
  • 7. G. Grätzer and H. Lakser, Three remarks on the arguesian identity, Notices Amer. Math. Soc. 20 (1973), pp. A-253, A-313, A-314.
  • 8. P. Gumm, A cancellation theorem for finite algebras, 1976 (manuscript).
  • 9. P. Gumm, Algebras in congruence permutable varieties: Geometrical properties of affine algebras, Algebra Universalis 8 (1978).
  • 10. J. Hagemann and Ch. Herrmann, A concrete ideal multiplication for algebraic systems and its relation with congruence distributivity, 1977 (manuscript).
  • 11. G. Hutchinson, Modular lattices and abelian categories, J. Algebra 19 (1971), 156-184.
  • 12. F. W. Lawvere, Functional semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-873.
  • 13. F. W. Lawvere, The category of categories as a foundation for mathematics, Proc. Conf. on Categorical Algebra, Springer-Verlag, New York, 1966, pp. 1-21.
  • 14. S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New York and Berlin, 1971.
  • 15. A. I. Mal'cev, On the general theory of algebraic systems, Mat. Sb. (N. S.) 35 (77) (1954), 3-20. (Russian)
  • 16. E. G. Manes, Algebraic theories, Graduate Texts in Math., Springer-Verlag. New York, 1975.
  • 17. E. G. Manes, Review of "Topological Transformation Groups. I", by J. de Vries, Bull. Amer. Math. Soc. 83 (1977), 720-731.
  • 18. B. Mitchell, Theory of categories, Academic Press, New York, 1965.
  • 19. A. Pultr and V. Trnková, Full embeddings, North-Holland, Amsterdam, 1978.
  • 20. W. Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33-53.