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The structure sheaf of an incidence algebra

Published online by Cambridge University Press:  09 April 2009

Beth Goldston Barnwell  and
A. C. Mewborn
Beth Goldston Barnwell
Affiliation:
Randolph Macon Womans CollegeLynchburg, Virginia, USA
A. C. Mewborn
Affiliation:
University of North CarolinaChapel Hill, North Carolina, USA
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Abstract

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Let R be the incidence algebra of a finite partially ordered set T over a commutative noetherian ring A. Then the spectrum of R is homeomorphic to the product (Spec A) x T, where Spec A has the usual Zariski topology and T has the order topology. An explicit construction is given for the structure sheaf of R over its spectrum.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 92 - 102
Copyright
Copyright © Australian Mathematical Society 1978

References

Goldston, B. and Mewborn, A. C. (1975), “A structure sheaf for a non-commutative noetherian ring”, Bull. Amer. Math. Soc. 81, 944–946.CrossRefGoogle Scholar
Goldston, B. and Mewborn, A. C. (1977), “A structure sheaf for a noncommutative noetherian ring”, J. Algebra 47, 18–28.Google Scholar
Gordon, R. and Robson, J. C. (1973), Krull Dimension (Mem. Amer. Math. Soc. 133, Providence, R.I., U.S.A.)CrossRefGoogle Scholar
Stenström, B. T. (1971), Rings and Modules of Quotients (Lecture Notes in Mathematics 237, Springer-Verlag, Berlin).Google Scholar