The Jacobson radical of the endomorphism ring of a projective module.
Abstract: In a recently published paper , the elements of the Jacobson radical of a ring of row-finite matrices over an arbitrary ring are characterized as those matrices with entries in the Jacobson radical of 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 0157984, https://doi.org/10.1090/S0002-9947-1960-0157984-8
-  Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. 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 0238889, https://doi.org/10.1090/S0002-9947-1969-0238889-9
- 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)
- J. Lambek, Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. MR 34 #5857. MR 0206032 (34:5857)
- 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)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16.30
Retrieve articles in all journals with MSC: 16.30
Keywords: Projective modules, Jacobson radical, endomorphism ring, row-finite matrices, vanishing set of ideals
Article copyright: © Copyright 1970 American Mathematical Society