Subrings of K[y1, …, yt] of the type D + I

AbstractIn this paper we consider the affine domain R = K[y1, …, y1] (where K is a field) having krull dimension n > 0 and subrings of R of the form S = D + I (where D is a subring of K and I is a nonzero proper ideal of R). In Section 1 we characterize when S is Noetherian. In Section 2 we determine when S is a Zero-divisor ring and when S is a Laskerian ring. We prove in Section 3 that S is a strong S-ring if and only if D is a strong S-ring and K is algebraic over D. We determine in Section 4 when S is an N-ring