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Endomorphism Semigroups of Sums of Rings

Published online by Cambridge University Press:  20 November 2018

Carlton J. Maxson
Carlton J. Maxson*
Affiliation:
Mathematics Department, Texas A & M University, College Station, Texas77843
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Let R= 〈R, +, •〉 be the cartesian sum of the rings Ri, i= 1, 2,…, n denoted by , and recall that R is a ring under the componentwise operations. It is well-known (e.g. [1], p. 212) that the endomorphisms of the group 〈R, + 〉 form a ring HomZR (under function addition and composition) and moreover HomZR is isomorphic to the matrix ring under the usual matrix operations of addition and multiplication.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 247 - 250
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Fuchs, L., Abelian Groups, Pergamon Press, New York, 1967.Google Scholar
2. Goldhaber, J. and Ehrlich, G., Algebra, The Macmillan Company, New York, 1970.Google Scholar
3. Herstein, I., Noncommutative Rings, Cams Monograph No. 15, MAA, 1968.Google Scholar