On perfect simpleinjective rings
Authors:
W. K. Nicholson and M. F. Yousif
Journal:
Proc. Amer. Math. Soc. 125 (1997), 979985
MSC (1991):
Primary 16D50, 16L30
MathSciNet review:
1363179
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Abstract: Harada calls a ring right simpleinjective if every homomorphism with simple image from a right ideal of to is given by left multiplication by an element of . In this paper we show that every left perfect, left and right simpleinjective ring is quasiFrobenius, extending a well known result of Osofsky on selfinjective rings. It is also shown that if is left perfect and right simpleinjective, then is quasiFrobenius if and only if the second socle of is countably generated as a left module, extending many recent results on selfinjective rings. Examples are given to show that our results are nontrivial extensions of those on selfinjective rings.
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Additional Information
W. K. Nicholson
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Email:
wknichol@acs.ucalgary.ca
M. F. Yousif
Affiliation:
Department of Mathematics, Ohio State University, Lima, Ohio 45804
Email:
yousif.1@osu.edu
DOI:
http://dx.doi.org/10.1090/S0002993997036782
PII:
S 00029939(97)036782
Keywords:
Perfect ring,
selfinjective ring,
quasiFrobenius ring
Received by editor(s):
April 24, 1995
Received by editor(s) in revised form:
October 11, 1995
Additional Notes:
The research of both authors was supported by NSERC Grant 8075 and by the Ohio State University.
Dedicated:
Dedicated to Professor K. Varadarajan on the occasion of his sixtieth birthday
Communicated by:
Ken Goodearl
Article copyright:
© Copyright 1997
American Mathematical Society
