Subvarieties of BL-algebras generated by single-component chains

• DOI: 10.1007/s001530100114
• Publication Date: 2004-03-18T21:24:03Z
• Authors: Antonio Di Nola; Francesc Esteva; Pere Garcia; Lluís Godo; Salvatore Sessa
• Keywords: variety; BL-algebras; BL-Algebra; Equational characterization; 0202 electrical engineering, electronic engineering, information engineering; BL-Algebra; variety; mv-algebra; 02 engineering and technology; Subvarieties; mv-algebra

The authors thank Petr Hájek for useful remarks and suggestions. The authors have been partially supported by the bilateral Italian-Spanish cooperation project Integrated Action HI 1998-0090<br/>In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called Å?âˆ?G.<br/>Peer Reviewed<br/>