Geodesic
General Heredity and Strength for Radical Classes
Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1410-1421

Voir la notice de l'article provenant de la source Cambridge University Press

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 thereexists a subring A of R such that AσR and Af = B. 
Sands, A. D.; Stewart, P. N. General Heredity and Strength for Radical Classes. Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1410-1421. doi: 10.4153/CJM-1988-064-5
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