Goodearl, Kenneth R.; Lenagan, T. H. Constructing bad Noetherian local domains using derivations. (English) Zbl 0692.13005 J. Algebra 123, No. 2, 478-495 (1989). This paper contains an explicit construction of commutative noetherian local domains R of dimension 1 or 2 having the integral closure infinitely generated as an R-module. Such examples are constructed having arbitrary embedding dimension and multiplicity. Moreover, R supports a derivation leaving no ideals invariant. The method is to define a subring R of a power series algebra by using a derivation. The computations required to show that R has the desired properties are rather straightforward. Reviewer: M.Cipu Cited in 1 ReviewCited in 10 Documents MSC: 13E05 Commutative Noetherian rings and modules 13B10 Morphisms of commutative rings 13G05 Integral domains 13H99 Local rings and semilocal rings Keywords:noetherian local domains; integral closure; multiplicity; power series algebra; derivation PDFBibTeX XMLCite \textit{K. R. Goodearl} and \textit{T. H. Lenagan}, J. Algebra 123, No. 2, 478--495 (1989; Zbl 0692.13005) Full Text: DOI References: [1] Akizuki, Y., Einige Bemerkungenu¨ber prima¨re Integrita¨tsbereiche mit Teilerkettensatz, (Proc. Phys.-Math. Soc. Japan, 17 (1935)), 327-336 · JFM 61.1029.02 [2] de Souza Doering, A. M.; Lequain, Y., Maximally differential prime ideals, J. Algebra, 101, 403-417 (1986) · Zbl 0591.13018 [3] Ferrand, D.; Raynaud, M., Fibres formelles d’un anneau local noethe´rien, Ann. Sci.E´cole Norm. Sup., 3, 295-311 (1970), (4) · Zbl 0204.36601 [4] Lequain, Y., Differential simplicity and complete integral closure, Pacific J. Math., 36, 741-751 (1971) · Zbl 0188.09702 [5] Nagata, M., Local Rings (1962), Interscience: Interscience New York · Zbl 0123.03402 [6] Seidenberg, A., Derivations and integral closure, Pacific J. Math., 16, 167-173 (1966) · Zbl 0133.29202 [7] Vasconcelos, W. V., Derivations of commutative noetherian rings, Math. Z., 112, 229-233 (1969) · Zbl 0181.05201 [8] Zariski, O.; Samuel, P., (Commutative Algebra, Vol. I (1958), Van Nostrand: Van Nostrand Princeton, NJ) · Zbl 0112.02902 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.