Studia Logica 104 (5):849-867 (2016)

Abstract
In any variety of bounded integral residuated lattice-ordered commutative monoids the class of its semisimple members is closed under isomorphic images, subalgebras and products, but it is not closed under homomorphic images, and so it is not a variety. In this paper we study varieties of bounded residuated lattices whose semisimple members form a variety, and we give an equational presentation for them. We also study locally representable varieties whose semisimple members form a variety. Finally, we analyze the relationship with the property “to have radical term”, especially for k-radical varieties, and for the hierarchy of varieties k>0 defined in Cignoli and Torrens.
Keywords Residuated lattices  Semisimple and local residuated lattices  k-Radical varieties  Radical term
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11225-016-9655-2
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,290
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

Bounded BCK‐Algebras and Their Generated Variety.Joan Gispert & Antoni Torrens - 2007 - Mathematical Logic Quarterly 53 (2):206-213.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Every Free Biresiduated Lattice is Semisimple.H. Takamura - 2003 - Reports on Mathematical Logic:125-133.
Bounded BCK‐Algebras and Their Generated Variety.Joan Gispert & Antoni Torrens - 2007 - Mathematical Logic Quarterly 53 (2):206-213.
Bounded BCK-Algebras and Their Generated Variety.J. D. Gispert & Antoni Torrens Torrell - 2007 - Mathematical Logic Quarterly 53 (2):206-213.

Analytics

Added to PP index
2016-02-19

Total views
13 ( #772,437 of 2,519,270 )

Recent downloads (6 months)
1 ( #407,861 of 2,519,270 )

How can I increase my downloads?

Downloads

My notes