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Overrings and dimensions of general \(D+M\) constructions. (English) Zbl 0621.13010

The D\(+M\) construction, developed by Gilmer, is a versatile tool for building integral domains with varied properties. There have been several studies involving more general analogues of this construction, and the paper under review is a continuation of one such study [see J. W. Brewer and E. A. Rutter, Mich. Math. J. 23, 33-42 (1976; Zbl 0318.13007)].
The general setup is as follows: T is an integral domain which is a direct sum of a subfield L and a maximal ideal M of T; D is a subring of L and \(R=D+M\). The authors sharpen results on the prime ideal structure in R, determine in terms of T, D and L, conditions under which R has the QR-property, and relate the dimension sequence of R to those of D and T under the assumption that \(T_ M\) is a valuation domain.
Reviewer: I.J.Papick

MSC:

13G05 Integral domains
13A15 Ideals and multiplicative ideal theory in commutative rings
13B02 Extension theory of commutative rings

Citations:

Zbl 0318.13007
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