English

Balanced d-lattices are complemented

Rings and Algebras 2007-05-23 v1

Abstract

We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is the characterization of d-lattices (a class of bounded lattices including the bounded distributive lattices, originally defined by a property of their compact congruences) as exactly those lattices in which all maximal filters/ideals are prime.

Keywords

Cite

@article{arxiv.math/0111282,
  title  = {Balanced d-lattices are complemented},
  author = {Martin Goldstern and Miroslav Ploscica},
  journal= {arXiv preprint arXiv:math/0111282},
  year   = {2007}
}

Comments

4 pages, LaTeX2e