The aim of this paper is to lay down some facts and techniques that are useful in order to describe the lattice of subvarieties of BL-algebras. The results include: a description of subalgebras and homomorphic images of totally ordered BL-algebras in terms of ordinal sums; a characterization of generic BL-algebras, i.e. the totally ordered BL-algebras that generate the whole variety; a full description of the subdirectly irreducible members of the variety generated by ordinal sums of finitely many Wajsberg hoops.
Agliano', P., Montagna, F. (2003). Varieties of BL- algebras I: General properties. JOURNAL OF PURE AND APPLIED ALGEBRA, 181(2-3), 105-129 [10.1016/S0022-4049(02)00329-8].
Varieties of BL- algebras I: General properties.
AGLIANO', PAOLO;MONTAGNA, FRANCO
2003-01-01
Abstract
The aim of this paper is to lay down some facts and techniques that are useful in order to describe the lattice of subvarieties of BL-algebras. The results include: a description of subalgebras and homomorphic images of totally ordered BL-algebras in terms of ordinal sums; a characterization of generic BL-algebras, i.e. the totally ordered BL-algebras that generate the whole variety; a full description of the subdirectly irreducible members of the variety generated by ordinal sums of finitely many Wajsberg hoops.
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https://hdl.handle.net/11365/7108