Strict Shells

Arthur Knoebel ()

Chapter IX in Sheaves of Algebras over Boolean Spaces, 2012, pp 235-260 from Springer

Abstract: Abstract The hypothesis that shells be Baer–Stone is rather restrictive. We weaken it, but to obtain a theorem comparable to that of the previous chapter, we must also weaken the previous conclusion: the representation is only as a subalgebra of the algebra of all global sections of a sheaf, rather than as an isomorphic image. The stalks still have no divisors of zero.The first section proves the theorem just summarized, for algebras that have only a multiplication and a nullity, called strict half-shells. We assume these half-shells have no nilpotents and satisfy null-symmetry, a collection of implications between products that are zero.The second section starts by exploring the consequence of having no divisors of zero when the sheaf is a Boolean product: the enveloping half-shell is then Baer–Stone. When the sheaf space is extremal disconnected, the enveloping half-shell is completely Baer–Stone.The third section adds a unity and an addition that is loop to the half-shell; this makes for stronger and simpler conclusions. We apply it to clusters.

Keywords: Prime Ideal; Commutative Ring; Factor Ideal; Ring Theory; Regular Ring (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4642-4_9

Ordering information: This item can be ordered from
http://www.springer.com/9780817646424

DOI: 10.1007/978-0-8176-4642-4_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().