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The radical equation P(An) = (P(A))n

Published online by Cambridge University Press:  20 January 2009

R. E. Propes
R. E. Propes
Affiliation:
The University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
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The purpose of this paper is to impose conditions on a radical class P so that the P-radical of the ring of n × n-matrices over a ring A is equal to the ring of n×n-matrices over the ring P(A). In (1), Amitsur gave such conditions, but with the stipulation that the radical class P contained all zero-rings (rings in which all products are zero). In what follows, we shall be working within the class of associative rings.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 3 , March 1975 , pp. 257 - 259
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1) Amitsur, S., A general theory of radicals II, Amer. J. Math. 76 (1954), 100–125.CrossRefGoogle Scholar
(2) Divinsky, N., Krempa, J. and Sulinski, A., Strong radical properties of alterna- tive and associative rings, J. Algebra 17 (1971), 369–388.CrossRefGoogle Scholar
(3) Jaegermann, M., Morita contexts and radicals, Bull. Acad. Polon. Sci, Ser Sci. Math. Astronom. Phys. 20 (1972), 619–623.Google Scholar
(4) Snider, R., Lattices of radicals, Pacific J. Math. 40 (1972), 207–220.CrossRefGoogle Scholar