The Jacobson radical of the endomorphism ring of a projective module.
Authors:
R. Ware and J. Zelmanowitz
Journal:
Proc. Amer. Math. Soc. 26 (1970), 15-20
MSC:
Primary 16.30
DOI:
https://doi.org/10.1090/S0002-9939-1970-0262281-8
MathSciNet review:
0262281
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Abstract | References | Similar Articles | Additional Information
Abstract: In a recently published paper [3], the elements of the Jacobson radical of a ring of row-finite matrices over an arbitrary ring $R$ are characterized as those matrices with entries in the Jacobson radical of $R$ which have a vanishing set of column ideals. In this paper, the characterization is extended to include the endomorphism ring of an arbitrary projective module. In the process we offer a greatly simplified proof of the theorem for row-finite matrices.
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI https://doi.org/10.1090/S0002-9947-1960-0157984-8
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- N. E. Sexauer and J. E. Warnock, The radical of the row-finite matrices over an arbitrary ring, Trans. Amer. Math. Soc. 139 (1969), 287–295. MR 238889, DOI https://doi.org/10.1090/S0002-9947-1969-0238889-9
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Keywords:
Projective modules,
Jacobson radical,
endomorphism ring,
row-finite matrices,
vanishing set of ideals
Article copyright:
© Copyright 1970
American Mathematical Society