A correspondence theorem for projective modules and the structure of simple Noetherian rings

Faith, Carl

doi:10.1090/S0002-9904-1971-12684-8

Author: Carl Faith
Journal: Bull. Amer. Math. Soc. 77 (1971), 338-342
MSC (1970): Primary 16A46; Secondary 15A50
DOI: https://doi.org/10.1090/S0002-9904-1971-12684-8
Errata, Volume 77: Bull. Amer. Math. Soc., Volume 77, Number 6 (1971), 1120--1120
MathSciNet review: 0280534
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References | Similar Articles | Additional Information

1962. H. Bass, The Morita theorems, Lecture Notes Published by the Mathematics Department, University of Oregon, Eugene, Ore., 1962.

Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
Carl Faith, Noetherian simple rings, Bull. Amer. Math. Soc. 70 (1964), 730–731. MR 167500, DOI https://doi.org/10.1090/S0002-9904-1964-11193-9
Carl Faith, A general Wedderburn theorem, Bull. Amer. Math. Soc. 73 (1967), 65–67. MR 202763, DOI https://doi.org/10.1090/S0002-9904-1967-11642-2
Carl Faith, Algebra: rings, modules and categories. I, Springer-Verlag, New York-Heidelberg, 1973. Die Grundlehren der mathematischen Wissenschaften, Band 190. MR 0366960
G. D. Findlay and J. Lambek, A generalized ring of quotients. I, II, Canad. Math. Bull. 1 (1958), 77–85, 155–167. MR 94370, DOI https://doi.org/10.4153/CMB-1958-009-3
A. W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3) 8 (1958), 589–608. MR 103206, DOI https://doi.org/10.1112/plms/s3-8.4.589
A. W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Soc. (3) 10 (1960), 201–220. MR 111766, DOI https://doi.org/10.1112/plms/s3-10.1.201
Kwangil Koh, On simple rings with maximal annihilator right ideals, Canad. Math. Bull. 8 (1965), 667–668. MR 227223, DOI https://doi.org/10.4153/CMB-1965-050-6
L. Lesieur and R. Croisot, Sur les anneaux premiers noethériens à gauche, Ann. Sci. École Norm. Sup. (3) 76 (1959), 161–183 (French). MR 0109166
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
Claudio Procesi, Sopra un teorema di Goldie riguardante la struttura degli anelli primi con condizioni di massimo, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 34 (1963), 372–377 (Italian). MR 158908