Balanced d-lattices are complemented

• Autorzy: Martin Goldstern , Miroslav Ploščica
• Języki publikacji: EN

Abstrakty

EN

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

Słowa kluczowe

EN

balanced congruence; balanced lattice; d-lattice; prime ideal; maximal ideal

Kategorie tematyczne

• 06B10: Ideals, congruence relations
• 08A30: Subalgebras, congruence relations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 33-37

Daty

wydano

2002

otrzymano

2001-12-03

Twórcy

autor

Martin Goldstern

• Technische Universität Wien, Institut für Algebra und Computermathematik, Wiedner Hauptstraße 8-10/118, A-1040 Wien, Austria

autor

Miroslav Ploščica

• Mathematical Institute, Slovak Academy of Sciences, Gresákova 6, 04001 Košice, Slovakia

Bibliografia

• [1] I. Chajda and G. Eigenthaler, Balanced congruences, Discuss. Math. - Gen. Algebra App. 21 (2001), 105-114.
• [2] G. Grätzer, General Lattice Theory (the second edition), Birkhäuser Verlag, Basel 1998.

Identyfikatory

DOI

10.7151/dmgaa.1045