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A characterization of generalized Hughes complexes

Published online by Cambridge University Press:  24 October 2008

R. Y. Sharp
Affiliation:
Pure Mathematics Section, The University, Sheffield S3 7RH
M. Tousi
Affiliation:
Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395–1795, Tehran, Iran

Extract

While trying to place the grade-theoretic analogue of the Cousin complex (for a commutative Noetherian ring A) of K. R. Hughes [7], and the complexes of modules of generalized fractions studied by the first author and H. Zakeri[18], and by L. O'Carroll [10, p. 420], on a similar footing, Sharp and M. Yassi[15] introduced the concept of generalized Hughes complex. Such complexes are described as follows.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Bǎnicǎ, C. and Stǎnǎşilǎ, O.. Algebraic methods in the global theory of complex spaces (Wiley, London, 1976).Google Scholar
[2]Bijan-Zadeh, M. H.. Torsion theories and local cohomology over commutative Noetherian rings. J. London Math. Soc. (2) 19 (1979), 402410.CrossRefGoogle Scholar
[3]Gabriel, P.. Des catégories abéliennes. Bull. Soc. Math. France 90 (1962), 323448.Google Scholar
[4]Gibson, G. J. and O'carroll, L.. Direct limit systems, generalized fractions and complexes of Cousin type. J. Pure and Applied Algebra 54 (1988), 249259.CrossRefGoogle Scholar
[5]Hamieh, M. A. and Zakeri, H.. Denominator systems and modules of generalized fractions. J. London Math. Soc. (2) 33 (1986), 237244.CrossRefGoogle Scholar
[6]Hartshorne, R.. Residues and duality, Lecture Notes in Mathematics 20 (Springer, Berlin, 1966).CrossRefGoogle Scholar
[7]Hughes, K. R.. A grade-theoretic analogue of the Cousin complex. Quaestiones Math. 9 (1986), 293300.CrossRefGoogle Scholar
[8]Kersken, M.. Cousinkomplex und Nennersysteme. Math. Zeit. 182 (1983), 389402.CrossRefGoogle Scholar
[9]Matsumura, H.. Commutative ring theory (Cambridge University Press, 1986).Google Scholar
[10]O'Carroll, L.. On the generalized fractions of Sharp and Zakeri. J. London Math. Soc. (2) 28 (1983), 417427.CrossRefGoogle Scholar
[11]Sharp, R. Y.. The Cousin complex for a module over a commutative Noetherian ring. Math. Zeit. 112 (1969), 340356.CrossRefGoogle Scholar
[12]Sharp, R. Y.. A Cousin complex characterization of balanced big Cohen-Macaulay modules. Quart. J. Math. Oxford (2) 33 (1982), 471485.CrossRefGoogle Scholar
[13]Sharp, R. Y. and Schenzel, P.. Cousin complexes and generalized Hughes complexes. Proc. London Math. Soc. (3) 68 (1994), 499517.CrossRefGoogle Scholar
[14]Sharp, R. Y. and Tang, Zhongming. On the structure of Cousin complexes. J. Math. Kyoto Univ. 33 (1993), 285297.Google Scholar
[15]Sharp, R. Y. and Yassi, M.. Generalized fractions and Hughes' grade-theoretic analogue of the Cousin complex. Glasgow Math. J. 32 (1990), 173188.CrossRefGoogle Scholar
[16]Sharp, R. Y. and Zakeri, H.. Modules of generalized fractions. Mathematika 29 (1982), 3241.CrossRefGoogle Scholar
[17]Sharp, R. Y. and Zakeri, H.. Local cohomology and modules of generalized fractions. Mathematika 29 (1982), 296306.CrossRefGoogle Scholar
[18]Sharp, R. Y. and Zakeri, H.. Modules of generalized fractions and balanced big Cohen-Macaulay modules. In Commutative algebra: Durham 1981. London Mathematical Society Lecture Notes 72 (Cambridge University Press, 1982), pp. 6182.Google Scholar
[19]Suominen, K.. Localization of sheaves and Cousin complexes. Acta Mathematica 131 (1973), 2741.CrossRefGoogle Scholar
[20]Yassi, M.. The generalized Hughes complex and modules of generalized fractions. PhD Thesis, University of Sheffield, 1989.Google Scholar