| Title:
|
Primes, coprimes and multiplicative elements (English) |
| Author:
|
Janowitz, Melvin F. |
| Author:
|
Powers, R. C. |
| Author:
|
Riedel, T. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
607-615 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
complete lattices |
| Keyword:
|
completely distributive lattices |
| Keyword:
|
Galois connection |
| Keyword:
|
multiplicative elements |
| Keyword:
|
way-below relation |
| MSC:
|
06A15 |
| MSC:
|
06B23 |
| MSC:
|
06B35 |
| MSC:
|
06D10 |
| idZBL:
|
Zbl 1011.06009 |
| idMR:
|
MR1756539 |
| . |
| Date available:
|
2009-01-08T18:55:52Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119117 |
| . |
| Reference:
|
[1] Birkhoff G.: Lattice Theory.American Mathematical Society, Providence RI, 1948. Zbl 0537.06001, MR 0029876 |
| Reference:
|
[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 |
| Reference:
|
[3] Dwinger P.: Unary operations on completely distributive complete lattices.Springer Lecture Notes in Math. 1149 (1985), 46-81. Zbl 0575.06011, MR 0823006 |
| Reference:
|
[4] Gratzer G.A.: Lattice theory; first concepts and distributive lattices.W.H. Freeman, San Francisco, 1971. MR 0321817 |
| Reference:
|
[5] Raney G.N.: Completely distributive complete lattices.Proc. Amer. Math. Soc. 3 (1952), 677-680. Zbl 0049.30304, MR 0052392 |
| Reference:
|
[6] Zhao D.: Semicontinuous lattices.Algebra Universalis 37 (1997), 458-476. Zbl 0903.06005, MR 1465303 |
| . |
