Coordinatization of lattices by regular rings without unit and Banaschewski functions
نویسندگان
چکیده
منابع مشابه
Coordinatization of lattices by regular rings without unit and Banaschewski functions
A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. We prove a set of results that include the following: • Every countable complemented modular lattice has a Banaschewski function with Boolean range, the latter being unique up to isomorphism. • Every (not necessarily unital) countable von Neumann regular ring R has a map ε ...
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The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...
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Themain aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have gen...
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2010
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-010-0088-x