Absolutely superficial sequences
- 1 January 1983
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 93 (1) , 35-47
- https://doi.org/10.1017/s0305004100060308
Abstract
Absolutely superficial sequences was introduced by P. Schenzel in order to study generalized Cohen-Macaulay (resp. Buchsbaum) modules. For an arbitrary local ring, they turned out to be d-sequences. This paper established properties of absolutely superficial sequences with respect to a module. It is shown that they are closely related to other sequences in the theory of generalized Cohen-Macaulay (resp. Buchsbaum) modules. In particular, there is a bounding function for the Hilbert-Samuel function of every parameter ideal such that this bounding function is attained if and only if the ideal is generated by an absolutely superficial sequenceKeywords
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This publication has 13 references indexed in Scilit:
- A characterization of two-dimensional unmixed local ringsMathematical Proceedings of the Cambridge Philosophical Society, 1981
- Some criteria for Buchsbaum modulesMonatshefte für Mathematik, 1980
- Remarks on generalized analytic independenceMathematical Proceedings of the Cambridge Philosophical Society, 1979
- Über superfizielle Systeme von ParameternMathematische Nachrichten, 1979
- Toward a Theory of Buchsbaum SingularitiesAmerican Journal of Mathematics, 1978
- Verallgemeinerte COHEN-MACAULAY-ModulnMathematische Nachrichten, 1978
- Generalized Analytic IndependenceProceedings of the American Mathematical Society, 1976
- Graded algebras of powers of ideals generated by A-sequencesJournal of Algebra, 1973
- Local Rings of High Embedding DimensionAmerican Journal of Mathematics, 1967
- Reductions of ideals in local ringsMathematical Proceedings of the Cambridge Philosophical Society, 1954