An additivity principle for p.i. rings

Amitsur, 1980, On the characteristic polynomial of a sum of matrices, Linear and Multilinear Algebra, 8, 177, 10.1080/03081088008817315 Amitsur, 1980, Prime ideals in P.I.-rings, J. Algebra, 62, 358, 10.1016/0021-8693(80)90188-X Artin, 1981, Integral ring homomorphisms, Adv. in Math., 39, 289, 10.1016/0001-8708(81)90005-0 Bergman, 1975, P.I. degrees and prime ideals, J. Algebra, 33, 435, 10.1016/0021-8693(75)90112-X Bourbaki, “Commutative Algebra,” Chap. V, p. 367, Exercise 17(c). Braun, 1979, Affine P.I. rings and their generalizations, J. Algebra, 58, 481, 10.1016/0021-8693(79)90174-1 Humphreys, 1975 Procesi, 1974, Finite-dimensional representations of algebras, Israel J. Math., 19, 169, 10.1007/BF02756630 Rowen, 1980 Schelter, 1976, Integral extensions of rings satisfying a polynomial identity, J. Algebra, 40, 245, 10.1016/0021-8693(76)90095-8