Geodesic
Primes, coprimes and multiplicative elements
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 607-615.

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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.
Classification : 06A15, 06B23, 06B35, 06D10
Keywords: complete lattices; completely distributive lattices; Galois connection; multiplicative elements; way-below relation 
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Janowitz, Melvin F.; Powers, R. C.; Riedel, T. Primes, coprimes and multiplicative elements. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 607-615. http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a0/