Bulletin of the American Mathematical Society

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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.

B. Banaschewski and E. Nelson, Equational compactness in equational classes of algebras, Algebra Universalis 2 (1972), 152–165. MR 308010, DOI 10.1007/BF02945023

Samuel Eilenberg and Saunders MacLane, Group extensions and homology, Ann. of Math. (2) 43 (1942), 757–831. MR 7108, DOI 10.2307/1968966

Samuel Eilenberg and Saunders MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294. MR 13131, DOI 10.1090/S0002-9947-1945-0013131-6

Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240

George Grätzer, General lattice theory, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 52, Birkhäuser Verlag, Basel-Stuttgart, 1978. MR 504338

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).

George Hutchinson, Modular lattices and abelian categories, J. Algebra 19 (1971), 156–184. MR 279154, DOI 10.1016/0021-8693(71)90103-7

F. William Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869–872. MR 158921, DOI 10.1073/pnas.50.5.869

F. William Lawvere, The category of categories as a foundation for mathematics, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 1–20. MR 0207517

Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872

A. I. Mal′cev, On the general theory of algebraic systems, Mat. Sb. N.S. 35(77) (1954), 3–20 (Russian). MR 0065533

Ernest G. Manes, Algebraic theories, Graduate Texts in Mathematics, No. 26, Springer-Verlag, New York-Heidelberg, 1976. MR 0419557

17.

E. G. Manes, Review of "Topological Transformation Groups. I", by J. de Vries, Bull. Amer. Math. Soc. 83 (1977), 720-731.

Barry Mitchell, Theory of categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965. MR 0202787

19.

A. Pultr and V. Trnková, Full embeddings, North-Holland, Amsterdam, 1978.

Walter Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33–53. MR 314726, DOI 10.1007/BF02945005

1.

B. Banaschewski and E. Nelson, Equational compactness in equational classes of algebras, Algebra Universalis 2 (1972), 152-165. MR 0308010

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