Bulletin of the American Mathematical Society

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Book Information:

Authors: Friedrich Kasch and Adolf Mader
Title: Rings, modules, and the total
Additional book information: Frontiers in Mathematics, Birkhäuser-Verlag, Basel, 2004, x+136 pp., ISBN 3-7643-7125-0, US$49.95$

Authors: 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., ISBN 0-521-83821-5, US$60.00$

Gorô Azumaya, On generalized semi-primary rings and Krull-Remak-Schmidt’s theorem, Jpn. J. Math. 19 (1948), 525–547. MR 32607

Gorô Azumaya, Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt’s theorem, Nagoya Math. J. 1 (1950), 117–124. MR 37832

Reinhold Baer, Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), 800–806. MR 2886, DOI 10.1090/S0002-9904-1940-07306-9

Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480

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

B. Eckmann and A. Schopf, Über injektive Moduln, Arch. Math. (Basel) 4 (1953), 75–78 (German). MR 55978, DOI 10.1007/BF01899665

Masatoshi Ikeda, A characterization of quasi-Frobenius rings, Osaka Math. J. 4 (1952), 203–209. MR 53085

N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. 67 (1945), 300–320. MR 12271, DOI 10.2307/2371731

T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999. MR 1653294, DOI 10.1007/978-1-4612-0525-8

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 96700

Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946

R. M. Thrall, Some generalization of quasi-Frobenius algebras, Trans. Amer. Math. Soc. 64 (1948), 173–183. MR 26048, DOI 10.1090/S0002-9947-1948-0026048-0

Robert Wisbauer, Foundations of module and ring theory, Revised and translated from the 1988 German edition, Algebra, Logic and Applications, vol. 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991. A handbook for study and research. MR 1144522

[Azu48]

Gorô Azumaya, On generalized semi-primary rings and Krull-Remak-Schmidt's theorem, Jap. J. Math. 19 (1948), 525-547. MR 0032607

[Azu50]

-, Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt's theorem, Nagoya Math. J. 1 (1950), 117-124. MR 0037832

[Bae40]

Reinhold Baer, Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), 800-806. MR 0002886

[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

[ES53]

B. Eckmann and A. Schopf, Über injektive Moduln, Arch. Math. 4 (1953), 75-78. MR 0055978

[Ike52]

Masatoshi Ikeda, A characterization of quasi-Frobenius rings, Osaka Math. J. 4 (1952), 203-209. MR 0053085

[Jac45]

N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. 67 (1945), 300-320. MR 0012271

[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

[Nak39]

Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611-633. MR 0000016

[Thr48]

R. M. Thrall, Some generalization of quasi-Frobenius algebras, Trans. Amer. Math. Soc. 64 (1948), 173-183. MR 0026048

[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