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Book Review
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Book Information
Author(s):
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(s):
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:
- 1.
- B. Banaschewski and E. Nelson, Equational compactness in equational classes of algebras, Algebra Universalis 2 (1972), 152-165. MR 308010
- 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.
- G. Grätzer, General lattice theory, Academic Press, New York; Birkhäuser Verlag, Basel; Akademie Verlag, Berlin, 1978. MR 504338
- 6.
- G. Grätzer, Universal algebra, 2nd expanded ed., Springer-Verlag, New York, 1978. 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.
- S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New York and Berlin, 1971. 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
Additional Information:
Reviewer(s):
G.
Grätzer
Review Information:
Journal:
Bull. Amer. Math. Soc.
84
(1978),
1339-1344.
DOI:
10.1090/S0002-9904-1978-14568-6
PII:
S 0002-9904(1978)14568-6
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