Prime and principal closed ideals in polynomial rings
Let R be a prime ring with maximal right quotient ring Q and extended centroid C. The main purpose of the paper under review is to characterise those prime ideals P of the polynomial ring R[x] which satisfy \(P\cap R=0\) as the ideals of the form Q[x]f\(\cap R[x]\), where f is an irreducible element of C[x]. Ideals of the latter form but with f not necessarily irreducible are termed principal closed ideals. The paper also includes results on rings intermediate between R and Q, a decomposition theorem for principal closed ideals and applications to results transferring certain properties from R to R[x].
scientific article; zbMATH DE number 4150422
scientific article