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General Heredity and Strength for Radical Classes

Published online by Cambridge University Press:  20 November 2018

A. D. Sands  and
P. N. Stewart
A. D. Sands
Affiliation:
The University of Dundee, Dundee, Scotland
P. N. Stewart
Affiliation:
Dalhousie University, Halifax, Nova Scotia
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An H-relation, as introduced by Rossa and Tangeman [4], is a relation σ on the class of associative rings with their subrings satisfying the following conditions:

(1) IσR implies that I is a subring of R;

(2) if IσR and f is a homomorphism of R, then (If)σ(Rf);

(3) if IσR and J is an ideal of R, then (I∩J)σJ.

Puczylowski [3] imposes also the condition

(4) if J is an ideal of R, then JσR.

A further condition satisfied by many familiar H-relations is the following:

(5) if f is a homomorphism from a ring R onto a ring S and BσS, then there exists a subring A of R such that AσR and Af = B.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1410 - 1421
Copyright
Copyright © Canadian Mathematical Society 1988

References

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