Abstract
In this paper, we explore some unexplored consequences of Agliano et al. (Studia Logica 87:73---98, 2007) and Agliano and Montagna (J Pure Appl Algebra 181:105---129, 2003) on varieties of BL-algebras and their hoop subreducts. The main topics are: generation by finite algebras, the finite embeddability property and varieties of finite index.
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