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Posets and differential graded algebras

Part of: Ordered sets

Published online by Cambridge University Press:  09 April 2009

Jacqui Ramagge  and
Wayne W. Wheeler
Jacqui Ramagge
Affiliation:
Mathematics Department University of NewcastleNSW 2308Australia e-mail: jacqui@maths.newcastle.edu.au
Wayne W. Wheeler
Affiliation:
Department of Mathematics University of GeorgiaAthens, GA 30602USA e-mail: www@alpha.math.uga.edu
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Abstract

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If P is a partially ordered set and R is a commutative ring, then a certain differential graded R-algebra A•(P) is defined from the order relation on P. The algebra A•() corresponding to the empty poset is always contained in A•(P) so that A•(P) can be regarded as an A•()-algebra. The main result of this paper shows that if R is an integral domain and P and P′ are finite posets such that A•(P)≅A•(P′) as differential graded A•()-algebras, then P and P′ are isomorphic.

MSC classification

Secondary: 06A06: Partial order, general

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 1 , February 1998 , pp. 1 - 19
Copyright
Copyright © Australian Mathematical Society 1998

References

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