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On Brown–McCoy radical classes in categories

Published online by Cambridge University Press:  20 January 2009

S. Veldsman
S. Veldsman
Affiliation:
Department of MathematicsRand Afrikaans UniversityP.O. Box 524Johannesburg 2000South Africa
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What does a simple ring with unity, a topological T0-space and a graph that has at most one loop but may possess edges, have in common? In this note we show that they all are Brown–McCoy semisimple. Suliński has generalised the well-known Brown–McCoy radical class of associative rings (cf. [1]) to a category which satisfies certain conditions. In [3] he defines a simple object, a modular class of objects and the Brown–McCoy radical class as the upper radical class determined by a modular class in a category which, among others, has a zero object and kernels. To include categories like that of topological spaces and graphs, we use the concepts of a trivial object and a fibre. We then follow Suliński and define a simple object, a modular class of objects and then the Brown–McCoy radical class as the upper radical class determined by a modular class.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 3 , October 1983 , pp. 337 - 341
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

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