Completely Primary Rings: II. Algebraic and Transcendental Extensions

We discuss in this paper the algebraic and transcendental extensions of completely primary rings. See the introduction of the author's paper "Completely Primary Rings I", published in this journal and referred to as CPI, for an introduction to the present paper. We continue the notations and conventions of CPI. Hence, the term ring always denotes a commutative, nonzero ring with unit element 1. If S is a ring, N(S) denotes its radical and H the natural homomorphism from S onto the residue class ring S/N(S) = S. If B is a subset of S B C S denotes the image of B under H. If B is a subring R of S, R is identified with R/N(R) and the contraction of H on R is considered as the natural homomorphism from R onto R/N(R).