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Book Review

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Book Information:

Author: Mario Petrich
Title: Categories of algebraic systems
Additional book information: Lecture Notes in Mathematics, vol. 553, Springer-Verlag, Berlin, Heidelberg, New York, 1976, viii + 217 pp., $10.20.

Author: Jonathan D. H. Smith
Title: Mal′cev varieties
Additional book information: Lecture Notes in Mathematics, vol. 554, Springer-Verlag, Berlin, Heidelberg, New York, 1976, viii + 156 pp., $7.40.

References [Enhancements On Off] (What's this?)

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  • 2. S. Eilenberg and S. Mac Lane, Group extensions and homology, Ann. of Math. (2) 43 (1942), 757-831. MR 7108
  • 3. S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294. MR 13131
  • 4. P. Freyd, Abelian categories, An introduction to the theory of functors, Harper & Row, New York, 1964. MR 166240
  • 5. George Grätzer, General lattice theory, Birkhäuser Verlag, Basel-Stuttgart, 1978. Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 52. MR 504338
  • 6. George Grätzer, Universal algebra, 2nd ed., Springer-Verlag, New York-Heidelberg, 1979. MR 538623
  • 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. MR 279154
  • 12. F. W. Lawvere, Functional semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-873. MR 158921
  • 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. MR 207517
  • 14. Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872
  • 15. A. I. Mal'cev, On the general theory of algebraic systems, Mat. Sb. (N. S.) 35 (77) (1954), 3-20. (Russian) MR 65533
  • 16. E. G. Manes, Algebraic theories, Graduate Texts in Math., Springer-Verlag. New York, 1975. MR 419557
  • 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. MR 202787
  • 19. A. Pultr and V. Trnková, Full embeddings, North-Holland, Amsterdam, 1978.
  • 20. W. Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33-53. MR 314726

Review Information:

Reviewer: G. Grätzer
Journal: Bull. Amer. Math. Soc. 84 (1978), 1339-1344
DOI: https://doi.org/10.1090/S0002-9904-1978-14568-6
American Mathematical Society