On the structure of generalized BL-algebras |
| |
Authors: | P. Jipsen F. Montagna |
| |
Affiliation: | (1) Department of Mathematics and Computer Science, Chapman University, Orange, CA 92866, USA;(2) Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini, 44 53100 Siena, Italy |
| |
Abstract: | A generalized BL - algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities . It is shown that all finite GBL-algebras are commutative, hence they can be constructed by iterating ordinal sums and direct products of Wajsberg hoops. We also observe that the idempotents in a GBL-algebra form a subalgebra of elements that commute with all other elements. Subsequently we construct subdirectly irreducible noncommutative integral GBL-algebras that are not ordinal sums of generalized MV-algebras. We also give equational bases for the varieties generated by such algebras. The construction provides a new way of order-embedding the lattice of -group varieties into the lattice of varieties of integral GBLalgebras. The results of this paper also apply to pseudo-BL algebras. This paper is dedicated to Walter Taylor. Received March 7, 2005; accepted in final form July 25, 2005. |
| |
Keywords: | 06F05 06D35 03G10 03G25 |
本文献已被 SpringerLink 等数据库收录! |
|