Regular congruence-preserving extensions of lattices |
| |
| Authors: | G Grätzer E T Schmidt |
| |
| Institution: | (1) Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada, e-mail: gratzer@cc.umanitoba.ca, URL: http://www.math.umanitoba.ca/homepages/gratzer/, CA;(2) Mathematical Institute of the Technical University of Budapest, Müegyetem rkp. 3, H-1521 Budapest, Hungary, e-mail: schmidt@math.bme.hu, URL: http://www.bme.math/~schmidt/, HU |
| |
| Abstract: | In this paper, we prove that every lattice L has a congruence-preserving extension into a regular lattice , moreover, every compact congruence of is principal. We construct by iterating a construction of the first author and F. Wehrung and taking direct limits.? We also discuss the case of a finite
lattice L, in which case can be chosen to be finite, and of a lattice L with zero, in which case can be chosen to have zero and the extension can be chosen to preserve zero.
Received September 10, 1999; accepted in final form October 16, 2000. |
| |
| Keywords: | and phrases: Regular lattice principal congruence compact congruence congruence-preserving embedding |
| 本文献已被 SpringerLink 等数据库收录！ |
|
