Primes, coprimes and multiplicative elements

Melvin F. Janowitz; Robert C. Powers; Thomas Riedel

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 607-615
  • ISSN: 0010-2628

Abstract

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The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.

How to cite

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Janowitz, Melvin F., Powers, Robert C., and Riedel, Thomas. "Primes, coprimes and multiplicative elements." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 607-615. <http://eudml.org/doc/248402>.

@article{Janowitz1999,
abstract = {The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.},
author = {Janowitz, Melvin F., Powers, Robert C., Riedel, Thomas},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {complete lattices; completely distributive lattices; Galois connection; multiplicative elements; way-below relation; complete lattice; completely distributive lattice; Galois connection; multiplicative element},
language = {eng},
number = {4},
pages = {607-615},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Primes, coprimes and multiplicative elements},
url = {http://eudml.org/doc/248402},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Janowitz, Melvin F.
AU - Powers, Robert C.
AU - Riedel, Thomas
TI - Primes, coprimes and multiplicative elements
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 607
EP - 615
AB - The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.
LA - eng
KW - complete lattices; completely distributive lattices; Galois connection; multiplicative elements; way-below relation; complete lattice; completely distributive lattice; Galois connection; multiplicative element
UR - http://eudml.org/doc/248402
ER -

References

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  1. Birkhoff G., Lattice Theory, American Mathematical Society, Providence RI, 1948. Zbl0537.06001MR0029876
  2. Gierz G., Hoffmann K.H., Keimel K., Mislove M., Scott D.S., A Compendium of Continuous Lattices, Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR0674650
  3. Dwinger P., Unary operations on completely distributive complete lattices, Springer Lecture Notes in Math. 1149 (1985), 46-81. (1985) Zbl0575.06011MR0823006
  4. Gratzer G.A., Lattice theory; first concepts and distributive lattices, W.H. Freeman, San Francisco, 1971. MR0321817
  5. Raney G.N., Completely distributive complete lattices, Proc. Amer. Math. Soc. 3 (1952), 677-680. (1952) Zbl0049.30304MR0052392
  6. Zhao D., Semicontinuous lattices, Algebra Universalis 37 (1997), 458-476. (1997) Zbl0903.06005MR1465303

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