When Is (K + I, K[y₁,…,y_t]) a Mori Pair?

Abstract

Let R = K[y ₁,…,y _t ] be an affine domain over a field K and I be a nonzero proper ideal of R. In Sec. 1 of this note, we characterize when (K + I, R) is a Mori pair. In Sec. 2 of this note, we prove the following theorem: Let A ⊆ B be domains such that C/Q is Mori for each subring C of B containing A and for any prime ideal Q of C. Then dim A − 1 ≤ dim B ≤ dim A + 1 and if dim A > 1 or dim B > 1 then dim A = dim B.

Key Words:

• Mori pair
• Residually Mori pair

Mathematics Subject Classification:

• Primary 13Exx
• Secondary 13Bxx

Acknowledgment

I am very much thankful to Professor D. K. Thakkar for his help in the preparation of this manuscript using LATEX.

Notes

^#Communicated by R. Parimala.