Previous |  Up |  Next


complete lattices; completely distributive lattices; Galois connection; multiplicative elements; way-below relation
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.
[1] Birkhoff G.: Lattice Theory. American Mathematical Society, Providence RI, 1948. MR 0029876 | Zbl 0537.06001
[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. MR 0674650
[3] Dwinger P.: Unary operations on completely distributive complete lattices. Springer Lecture Notes in Math. 1149 (1985), 46-81. MR 0823006 | Zbl 0575.06011
[4] Gratzer G.A.: Lattice theory; first concepts and distributive lattices. W.H. Freeman, San Francisco, 1971. MR 0321817
[5] Raney G.N.: Completely distributive complete lattices. Proc. Amer. Math. Soc. 3 (1952), 677-680. MR 0052392 | Zbl 0049.30304
[6] Zhao D.: Semicontinuous lattices. Algebra Universalis 37 (1997), 458-476. MR 1465303 | Zbl 0903.06005
Partner of
EuDML logo