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WHEN IS THE INTEGRAL CLOSURE COMPARABLE TO ALL INTERMEDIATE RINGS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 19 October 2016, pp. 14-21
- Print publication:
- February 2017
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- Article
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Let
$R\subset S$ be an extension of integral domains, with 
$R^{\ast }$ the integral closure of 
$R$ in 
$S$ . We study the set of intermediate rings between 
$R$ and 
$S$ . We establish several necessary and sufficient conditions for which every ring contained between 
$R$ and 
$S$ compares with 
$R^{\ast }$ under inclusion. This answers a key question that figured in the work of Gilmer and Heinzer [‘Intersections of quotient rings of an integral domain’, J. Math. Kyoto Univ.7 (1967), 133–150].
