Free algebras in varieties of BL-algebras generated by BLn-chains

Abstract

Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain which is an ordinal sum of a finite MV-chain ${\bf L}_n$ and a generalized BL-chain ${\bf B}$ are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of ${\bf L}_n$ and free algebras in the variety of basic hoops generated by ${\bf B}.$ The Boolean products are taken over the Stone spaces of the Boolean subalgebras of idempotents of free algebras in the variety of MV-algebras generated by ${\bf L}_n.$

Published: Journal of the Australian Mathematical Society, 80 (2006), 419-439.