Ali Jaballah – Intermediate Rings in Integral Extensions

University of Sharjah

Extensions of commutative rings
with finite sets of intermediate rings or finite chains of intermediate rings have obtained recently numerous satisfactory characterizations in several recent papers. There is also a steady progress in the computations of these quantities. An algorithm for computing the number of intermediate rings had been established for the case where A is an integrally closed domain and B is the quotient field of A. This had been then generalized for the case where is a normal pair and B is not necessarily the quotient field of A. Note that is called a normal pair if each intermediate ring T,
, is integrally closed in B. It has been also recently settled for not necessarily integrally closed domains. The length of chains of intermediate rings had been also computed for normal pairs. These problems remain however open for many other types of ring extensions. We investigate in this work the case of an integral extension and establish results giving the exact number and length of chains of intermediate rings.