On Sums of Radical and Regular Rings

We find conditions which ensure that a ring is adjoint regular provided that it is a sum of a radical subring with an adjoint regular subring. We also provide a criterion of adjoint regularity for a ring which is a sum of its radical and a regular subring.__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 71–75, 2003.