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Generating the variety of BL-algebras. (English) Zbl 1093.03039
Summary: This paper collects some results from previous work by P. Aglianó, I. M. A. Ferreirim and the author [see, e.g., P. Aglianó and the author, J. Pure Appl. Algebra 181, 105–129 (2003; Zbl 1034.06009]. Our purpose is to illustrate some interesting classes of algebras which generate the whole variety of BL-algebras. In particular, we prove that such a variety is generated by its finite members and by the class of finite ordinal sums of Łukasiewicz t-norm algebras. Finally, we characterize the BL-chains which generate the whole variety of BL-algebras.

MSC:
03G25 Other algebras related to logic
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