On the variety of M -generalized łukasiewicz algebras of order N

Studia Logica 94 (2):291-305 (2010)

Abstract
In this paper we pursue the study of the variety of m -generalized Łukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Łukasiewicz algebras of order n . Given , we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Łukasiewicz algebra of order n and for each congruence on A we find a description via the corresponding Stone filter. We characterize the principal congruences on A via Stone filters. In doing so, we obtain a polynomial equation which defines the principal congruences on the algebras of . After showing that for m > 1 and n > 2, the variety of Łukasiewicz algebras of order n is a proper subvariety of , we prove that is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability.
Keywords Łukasiewicz algebra of order n   m-generalized Łukasiewicz algebra of order n  finitely generated variety  discriminator variety  equationally definable principal congruences  congruence permutable variety  congruence uniform variety  congruence coherent variety  congruence regular variety  filtral variety
Categories (categorize this paper)
DOI 10.1007/s11225-010-9236-8
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,796
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Analytics

Added to PP index
2010-02-27

Total views
42 ( #188,628 of 2,244,034 )

Recent downloads (6 months)
12 ( #86,802 of 2,244,034 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature