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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the structure of semiprime rings

Author: Augusto H. Ortiz
Journal: Proc. Amer. Math. Soc. 38 (1973), 22-26
MSC: Primary 16A12; Secondary 16A21
MathSciNet review: 0313292
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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$.

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Keywords: Finiteness assumption, subdirect sums, radical property, primitive ideals, prime ideals, irreducible module, the prime radical, the Jacobson radical, hereditary radical, Prüfer module, essential submodule, small submodule, subdirectly irreducible, heart of a module, injective hull, quasi-injective hull, essential extension
Article copyright: © Copyright 1973 American Mathematical Society

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