|
A right PCI ring is right Noetherian
Author:
Robert F. Damiano
Journal:
Proc. Amer. Math. Soc. 77 (1979), 11-14
MSC:
Primary 16A46
MathSciNet review:
539620
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: C. Faith and J. Cozzens have shown that a ring, whose right proper cyclic modules are injective, is either semisimple or a simple, right semihereditary, right Ore V-domain. They have posed a question as to whether such a ring is right noetherian. In this paper, an affirmative answer is given to that question. Moreover, necessary and sufficient conditions are given as to when a right PCI ring is left PCI.
- [1]
John
Cozzens and Carl
Faith, Simple Noetherian rings, Cambridge University Press,
Cambridge, 1975. Cambridge Tracts in Mathematics, No. 69. MR 0396660
(53 #522)
- [2]
Lawrence
Levy, Torsion-free and divisible modules over
non-integral-domains, Canad. J. Math. 15 (1963),
132–151. MR 0142586
(26 #155)
- [3]
B.
L. Osofsky, Noninjective cyclic modules,
Proc. Amer. Math. Soc. 19 (1968), 1383–1384. MR 0231857
(38 #185), http://dx.doi.org/10.1090/S0002-9939-1968-0231857-7
- [4]
Bo
Stenström, Rings of quotients, Springer-Verlag, New York,
1975. Die Grundlehren der Mathematischen Wissenschaften, Band 217; An
introduction to methods of ring theory. MR 0389953
(52 #10782)
- [1]
- J. Cozzens and C. Faith, Simple noetherian rings, Cambridge Tracts in Math. and Math. Phys., University Press, Cambridge, 1975. MR 0396660 (53:522)
- [2]
- L. Levy. Torsion-free and divisible modules over nonintegral domains, Canad. J. Math., 15 (1963), 132-157. MR 0142586 (26:155)
- [3]
- B. Osofsky, Noninjective cyclic modules, Proc. Amer. Math. Soc. 19 (1968), 1383-1384. MR 0231857 (38:185)
- [4]
- B. Stenström, Rings of quotients, Springer-Verlag, Berlin and New York, 1975. MR 0389953 (52:10782)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
16A46
Retrieve articles in all journals
with MSC:
16A46
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0539620-1
PII:
S 0002-9939(1979)0539620-1
Article copyright:
© Copyright 1979 American Mathematical Society
|
