Jim Coykendall and Tiberiu Dumitrescu: On a certain ring construction, p.141-148

Abstract:

Let $D$ be an integral domain, $K$ a subset of $D$ and $(P_k)_{k\in K}$ a family of prime ideals of $D$ such that $j-k$ is invertible modulo $P_k$ for all $j,k\in K,j\neq k$. Beginning with this data, we construct an overring $E$ of the polynomial ring $D[x]$ such that every ideal $P_k$ is contained in a principal prime ideal of $E$.

Key Words: Integral domain, prime ideal.

2000 Mathematics Subject Classification: Primary: 13A15,
Secondary 13B22, 13F05.

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