Primes, coprimes and multiplicative elements
Janowitz, Melvin F. ; Powers, Robert C. ; Riedel, Thomas
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 607-615 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1999-01-01
Classification:  06A15,  06B23,  06B35,  06D10 
@article{119117,
     author = {Melvin F. Janowitz and Robert C. Powers and Thomas Riedel},
     title = {Primes, coprimes and multiplicative elements},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {607-615},
     zbl = {1011.06009},
     mrnumber = {1756539},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119117}
}

Janowitz, Melvin F.; Powers, Robert C.; Riedel, Thomas. Primes, coprimes and multiplicative elements. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 607-615. http://gdmltest.u-ga.fr/item/119117/

Birkhoff G. Lattice Theory, American Mathematical Society, Providence RI, 1948. | MR 0029876 | Zbl 0537.06001

Gierz G.; Hoffmann K.H.; Keimel K.; Mislove M.; Scott D.S. A Compendium of Continuous Lattices, Springer-Verlag, Berlin-Heidelberg-New York, 1980. | MR 0674650

Dwinger P. Unary operations on completely distributive complete lattices, Springer Lecture Notes in Math. 1149 (1985), 46-81. (1985) | MR 0823006 | Zbl 0575.06011

Gratzer G.A. Lattice theory; first concepts and distributive lattices, W.H. Freeman, San Francisco, 1971. | MR 0321817

Raney G.N. Completely distributive complete lattices, Proc. Amer. Math. Soc. 3 (1952), 677-680. (1952) | MR 0052392 | Zbl 0049.30304

Zhao D. Semicontinuous lattices, Algebra Universalis 37 (1997), 458-476. (1997) | MR 1465303 | Zbl 0903.06005