Laskerian pairs (Q1122628)

If T is a commutative ring and R a subring of T containing the unity of T, (R,T) is called a Laskerian pair (LP) if every ring A, \(R\subseteq A\subseteq T\) is Laskerian. Necessary and sufficient conditions are given for different pairs (R,T) to be a LP (e.g. (R,R[X]), where X is an indeterminate, (R,K), where K is a field, \((R,S^{-1}R)\), where R is a domain and S is a multiplicatively closed subset of R, etc.).