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Book Review
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Book Information
Author(s):
Friedrich Kasch and Adolf Mader
Title:
Rings, modules, and the total
Additional book information:
Frontiers in Mathematics,
Birkhäuser-Verlag, Basel,
2004,
x+136 pp.,
US$49.95,
ISBN 3-7643-7125-0
Author(s):
Robert R. Colby and Kent R. Fuller
Title:
Equivalence and duality for module categories, with tilting and cotilting for rings
Additional book information:
Cambridge Tracts in Mathematics,
Cambridge University Press, vol. 161, Cambridge,
2004,
x+152 pp.,
US$60.00,
ISBN 0-521-83821-5
References:
-
- [Azu48]
- Gorô Azumaya, On generalized semi-primary rings and Krull-Remak-Schmidt's theorem, Jap. J. Math. 19 (1948), 525-547. MR 0032607 (11:316d)
- [Azu50]
- -, Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt's theorem, Nagoya Math. J. 1 (1950), 117-124. MR 0037832 (12:314e)
- [Bae40]
- Reinhold Baer, Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), 800-806. MR 0002886 (2:126i)
- [CE56]
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, NJ, 1956. MR 0077480 (17:1040e)
- [EM45]
- Samuel Eilenberg and Saunders MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294. MR 0013131 (7:109d)
- [ES53]
- B. Eckmann and A. Schopf, Über injektive Moduln, Arch. Math. 4 (1953), 75-78. MR 0055978 (15:5d)
- [Ike52]
- Masatoshi Ikeda, A characterization of quasi-Frobenius rings, Osaka Math. J. 4 (1952), 203-209. MR 0053085 (14:719d)
- [Jac45]
- N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. 67 (1945), 300-320. MR 0012271 (7:2f)
- [Lam99]
- T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999. MR 1653294 (99i:16001)
- [Mor58]
- Kiiti Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83-142. MR 0096700 (20:3183)
- [Nak39]
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611-633. MR 0000016 (1:3a)
- [Thr48]
- R. M. Thrall, Some generalization of quasi-Frobenius algebras, Trans. Amer. Math. Soc. 64 (1948), 173-183. MR 0026048 (10:98c)
- [Wis91]
- Robert Wisbauer, Foundations of module and ring theory, German ed., Algebra, Logic and Applications, vol. 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991. A handbook for study and research. MR 1144522 (92i:16001)
Additional Information:
Reviewer(s):
Barbara
L.
Osofsky
Affiliation:
Rutgers University
Email:
osofsky@math.rutgers.edu.
Review Information:
Journal:
Bull. Amer. Math. Soc.
44
(2007),
475-480.
MSC
(2000):
Primary 16D10, 16-02;
Secondary 16D90, 16E30, 18E15
PII:
S 0273-0979(07)01144-5
Posted:
March 29, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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