On the structure of semiprime rings
HTML articles powered by AMS MathViewer
- by Augusto H. Ortiz
- Proc. Amer. Math. Soc. 38 (1973), 22-26
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313292-8
- PDF | Request permission
Abstract:
The structure of prime rings has recently been studied by A. W. Goldie, R. E. Johnson, L. Lesieur and R. Croisot. In their main results some sort of finiteness assumption is invariably made. It is shown in this paper that certain semiprime rings are subdirect sums of full rings of linear transformations of a right vector space over a division ring. No finiteness assumption is made about the ring. An apparently new radical property is defined and some of its properties are established; e.g., the radical of a matrix ring ${R_n}$ is the matrix ring of the radical of $R$.References
- V. A. Andrunakievič and Ju. M. Rjabuhin, Modules and radicals, Soviet Math. Dokl. 5 (1964), 728–731. MR 0190182 T. Chi-Te, Report on injective modules, Queen’s Papers in Pure and Appl. Math., no. 6, Queen’s University, Kingston, Ontario, 1966.
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
- Neal H. McCoy, The theory of rings, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0188241
- Edward T. Wong, Endomorphisms of the quasi-injective hull of a module, Canad. Math. Bull. 13 (1970), 149–150. MR 260790, DOI 10.4153/CMB-1970-034-x
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 22-26
- MSC: Primary 16A12; Secondary 16A21
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313292-8
- MathSciNet review: 0313292