Abstract
AbstractBijective correspondences are established between the radical classes R (in a variety W of rings) with the property that a ring A is in R exactly when its finitely generated subrings are all in R, and certain filters of ideals in a free W-ring. It follows that such classes are determined by the polynomial identities satisfied by the finite subsets of their members. Analogous considerations are applied to radical classes R which, for a fixed integer n, have the property that a ring is in R if and only if its subrings generated by at most n elements are in R.
Publisher
Cambridge University Press (CUP)
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