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Generalized fractions, Buchsbaum modules and generalized Cohen-Macaulay modules

Published online by Cambridge University Press:  24 October 2008

R. Y. Sharp  and
H. Zakeri
R. Y. Sharp
Affiliation:
University of Sheffield
H. Zakeri
Affiliation:
University for Teacher Education, Tehran
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Extract

Let A be a (commutative Noetherian) local ring (with identity) having maximal ideal m and positive dimension. This note is concerned with, among other things, a complex of A -modules which was studied in [8] and which involves modules of generalized fractions derived from A and subsets of systems of parameters for A; in ([8], 3·5), the complex was shown to have connections with local cohomology. The complex is described as follows.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 429 - 436
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Hamieh, M. A. and Sharp, R. Y.. Krull dimension and generalized fractions. Proc. Edinburgh Math. Soc. (to appear).Google Scholar
[2]Northcott, D. G.. An Introduction to Homological Algebra (Cambridge University Press, 1960).CrossRefGoogle Scholar
[3]O'Carkoll, L.. On the generalized fractions of Sharp and Zakeri. J. London Math. Soc. (2) 28 (1983), 417–427.CrossRefGoogle Scholar
[4]Renschxjch, B., Stückbad, J. and Vogel, W.. Weitere Bemerkungen zu einem Problem der Schnittheorie und über ein Maβ von A. Seidenberg für die Imperfektheit. J. Algebra 37 (1975), 447–471.CrossRefGoogle Scholar
[5]Schenzel, P., Trung, N. V. and Cuong, N. T.. Verallgemeinerte Cohen-Macaulay-Moduln. Math. Nachr. 85 (1978), 57–73.CrossRefGoogle Scholar
[6]Sharp, R. Y.. Local cohomology theory in commutative algebra. Quart. J. Math. Oxford (2) 21 (1970), 425–434.CrossRefGoogle Scholar
[7]Sharp, R. Y. and Zakeri, H.. Modules of generalized fractions. Mathematika 29 (1982), 32–41.CrossRefGoogle Scholar
[8]Sharp, R. Y. and Zakeri, H.. Local cohomology and modules of generalized fractions. Mathematika 29 (1982), 296–306.CrossRefGoogle Scholar
[9]Sharp, R. Y. and Zakert, H.. Modules of generalized fractions and balanced big Cohen-Macaulay modules. Commutative algebra: Durham 1981 (London Mathematical Society Lecture Notes 72, Cambridge University Press, 1982), pp. 61–82.Google Scholar
[10]Vocel, W.. A nonzero-divisor characterization of Buchsbaum modules. Michigan Math. J. 28 (1981), 147–152.Google Scholar