Subdirect sums, hereditary radicals, and structure spaces
Author:
A. G. Heinicke
Journal:
Proc. Amer. Math. Soc. 25 (1970), 29-33
MSC:
Primary 16.50
DOI:
https://doi.org/10.1090/S0002-9939-1970-0255609-6
MathSciNet review:
0255609
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Abstract | References | Similar Articles | Additional Information
Abstract: If a ring $K$ is subdirectly embedded into the product $S$ of a finite number of rings by a mapping $i$, then it is proved that $i(H(K)) = i(K) \cap H(S)$ for any hereditary radical $H$, and that any structure space of $K$ has the topology of a quotient space of a structure space of $S$.
- Nathan Divinsky, Rings and radicals, Mathematical Expositions, No. 14, University of Toronto Press, Toronto, Ont., 1965. MR 0197489
- John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
- G. Michler, Radicals and structure spaces, J. Algebra 4 (1966), 199–219. MR 197507, DOI https://doi.org/10.1016/0021-8693%2866%2990039-1
- E. Sąsiada and P. M. Cohn, An example of a simple radical ring, J. Algebra 5 (1967), 373–377. MR 202769, DOI https://doi.org/10.1016/0021-8693%2867%2990048-8
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Additional Information
Keywords:
Subdirect sum,
hereditary radical,
structure space,
Zariski topology
Article copyright:
© Copyright 1970
American Mathematical Society