A Brief History of Order Ideals

E. Graham Evans and Phillip Griffith ()
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E. Graham Evans: University of Illinois at Urbana Champaign, Department of Mathematics
Phillip Griffith: University of Illinois at Urbana Champaign, Department of Mathematics

A chapter in Commutative Algebra, 2013, pp 393-417 from Springer

Abstract: Abstract The notion of order ideal is no doubt implicit in a paper by Serre in 1958 on free summands of projective modules. A formal definition is given by Bass. However, any algebraist contemplating the question, “on what locus of prime ideals in Spec(R) does an element e in a module E generate a free summand?”, has in fact encountered the concept of an order ideal. In the account on order ideals and their applications in this paper, it is our intent to elaborate on four basic theorems - as we see them - that give insight into the height properties of these ideals. We do this both from a historical view as well as a view of their utility.

Keywords: Prime Ideal; Local Ring; Short Exact Sequence; Local Domain; Free Resolution (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-5292-8_12

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