×

Modules over Dedekind prime rings. (English) Zbl 0211.05603


MSC:

16N60 Prime and semiprime associative rings
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16P40 Noetherian rings and modules (associative rings and algebras)
Full Text: DOI

References:

[1] Auslander, M.; Goldman, O., Maximal orders, Trans. Amer. Math. Soc., 97, 1-24 (1960) · Zbl 0117.02506
[2] Bass, H., The Morita Theorems, (Mimeographed notes (1962), University of Oregon)
[3] Cartan, H.; Eilenberg, S., Homological Algebra (1956), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 0075.24305
[4] Chevalley, C., L’arithmétique dans les algèbres de matrices, Actual. Sci. Ind., No. 323 (1936), Paris · JFM 62.0102.01
[5] D. Eisenbud and J. C. RobsonJ. Algebra; D. Eisenbud and J. C. RobsonJ. Algebra · Zbl 0211.05701
[6] Goldie, A. W., Non-commutative principal ideal rings, Arch. Math., 13, 213-221 (1962) · Zbl 0101.27304
[7] Goldie, A. W., Rings with Maximum Condition, (Mimeographed notes (1961), Yale Univ) · Zbl 0091.03304
[8] W. D. Gwynne and J. C. Robson; W. D. Gwynne and J. C. Robson · Zbl 0227.16005
[9] K. M. Hunter; K. M. Hunter
[10] Jacobson, N., The theory of rings, Amer. Math. Soc. Math. Surveys II (1943), New York · Zbl 0060.07302
[11] Jacobson, N., Structure of rings, (Amer. Math. Soc. Colloq. Publ., 37 (1956)), New York · JFM 65.1131.01
[12] Kaplansky, I., Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc., 72, 327-340 (1952) · Zbl 0046.25701
[13] Kaplansky, I., Fields and Rings (1969), Univ. of Chicago Press: Univ. of Chicago Press Chicago
[14] Levy, L., Torsion-free and divisible modules over non-integral domains, Can. J. Math., 15, 132-151 (1963) · Zbl 0108.04001
[15] Littlewood, J. E., A Mathematician’s Miscellany (1953), Methuen: Methuen London · Zbl 0051.00101
[16] Rinehart, G. S., Note on the global dimension of a certain ring, (Proc. Amer. Math. Soc., 13 (1962)), 341-346 · Zbl 0104.26102
[17] Robson, J. C., Artinian quotient rings, (Proc. London Math. Soc., 17 (1967)), 600-616 · Zbl 0154.28803
[18] Robson, J. C., Non-commutative Dedekind rings, J. Algebra, 9, 249-265 (1968) · Zbl 0174.06801
[19] Swan, R. G., Projective modules over group rings and maximal orders, Ann. Math., 76, 55-61 (1962) · Zbl 0112.02702
[20] D. B. Webber; D. B. Webber · Zbl 0211.06201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.