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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
MathSciNet review: 0262281
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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.

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  • [1] H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 28 #1212. MR 0157984 (28:1212)
  • [2] J. Lambek, Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. MR 34 #5857. MR 0206032 (34:5857)
  • [3] 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 39 #249. MR 0238889 (39:249)

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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

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