Hostname: page-component-5f745c7db-6bmsf Total loading time: 0 Render date: 2025-01-06T11:21:19.389Z Has data issue: true hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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