Archimedean frames, revisited

Jorge Martinez

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 1, page 25-44
  • ISSN: 0010-2628

Abstract

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This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called joinfitness and is Choice-free. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an infinitesimal element arises naturally, and the join of suitably chosen infinitesimals defines the joinfit nucleus. The paper concludes with mostly Choice-free applications of these ideas to commutative rings and their radical ideals.

How to cite

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Martinez, Jorge. "Archimedean frames, revisited." Commentationes Mathematicae Universitatis Carolinae 49.1 (2008): 25-44. <http://eudml.org/doc/250453>.

@article{Martinez2008,
abstract = {This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called joinfitness and is Choice-free. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an infinitesimal element arises naturally, and the join of suitably chosen infinitesimals defines the joinfit nucleus. The paper concludes with mostly Choice-free applications of these ideas to commutative rings and their radical ideals.},
author = {Martinez, Jorge},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {archimedean lattice; joinfit coreflection; infinitesimals; fitness conditions; Archimedean lattice; joinfit coreflection; infinitesimals; fitness conditions},
language = {eng},
number = {1},
pages = {25-44},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Archimedean frames, revisited},
url = {http://eudml.org/doc/250453},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Martinez, Jorge
TI - Archimedean frames, revisited
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 1
SP - 25
EP - 44
AB - This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called joinfitness and is Choice-free. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an infinitesimal element arises naturally, and the join of suitably chosen infinitesimals defines the joinfit nucleus. The paper concludes with mostly Choice-free applications of these ideas to commutative rings and their radical ideals.
LA - eng
KW - archimedean lattice; joinfit coreflection; infinitesimals; fitness conditions; Archimedean lattice; joinfit coreflection; infinitesimals; fitness conditions
UR - http://eudml.org/doc/250453
ER -

References

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