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Commutation Problems Involving Rings of Infinite Matrices

Published online by Cambridge University Press:  20 January 2009

E. M. Patterson
E. M. Patterson
Affiliation:
King's CollegeAberdeen
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Let R be a ring and let J be the set of all integers. In the set M(R) of all mappings A: J×J→R, let addition and multiplication be defined by

Here aij denotes the image of (i, j) under A and bij, cij, dij are similarly defined for the mappings B, C, D. In (2) we require A, B to be such that the sum is defined and is in R. Thus, in general, M(R) is not closed with respect to multiplication.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 1 , June 1964 , pp. 55 - 60
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

REFERENCE

(1) Jacobson, N., Structure of Rings (American Math. Soc. Colloquium Publications XXXVII, New York, 1956).CrossRefGoogle Scholar
(2) Patterson, E. M., On the radicals of certain rings of infinite matrices, Proc. Roy. Soc. Edin. A, 65 (1961), 263–271.Google Scholar
(3) Patterson, E. M., On the radicals of rings of row-finite matrices, Proc. Roy. Soc. Edin. A, 66, 42–46.Google Scholar