Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 32 Issue 2
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- Pages.265-270
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- 1995
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
SOME EQUIDIMENSIONAL HILBERT RINGS
Abstract
Let $K_1, \ldots, K_n$ be fields of transcendence degrees $t_1, \ldots, t_n$ respectively over a common subfield F. O'Carroll and Qureshi [7] conjectured that the tensor product $R = K_1 \otimes K_2 \otimes \ldots \otimes K_n$ is an equidimensional Hilbert ring and proved the conjecture in special cases. Trung proved the conjecture [9] and O'Carroll, Bowman and Howie [3,5] generalized the Trung's result in two directions and obtained two theorems stated below.