J. Aust. Math. Soc.  80 (2006), 419-439
Free algebras in varieties of BL-algebras generated by a $\mathrm{BL}_n$-chain

Manuela Busaniche
  Departamento de Matemática
  Facultad de Ciencias Exactas y Naturales
  Universidad de Buenos Aires - CONICET
  Ciudad Universitaria, 1428 Buenos Aires
  Argentina
  manuelabusaniche@yahoo.com.ar
and
Roberto Cignoli
  Departamento de Matemática
  Facultad de Ciencias Exactas y Naturales
  Universidad de Buenos Aires - CONICET
  Ciudad Universitaria, 1428 Buenos Aires
  Argentina
  cignoli@mate.dm.uba.ar


Abstract
Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that 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 ${\bf L}_n$.
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