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The variety BL of BL-algebras is the algebraic counterpart of BL, the logicpresented by Hájek which includes a fragment common to the most importantfuzzy logics (Łukasiewicz, Gödel and product logics). Likewise many variety, BLis generated by its totally ordered members, namely BL-chains. Since everyBL-algebra can be embedded into the direct product of BL-chains and everyBL-chain can be decomposed as an ordinal sum of simpler structures, Jipsenand Montagna proposed in [3] a construction called poset product as a sort ofgeneralization of direct product and ordinal sum.In [2], based on the results of [4], it is shown that every BL-algebra is asubalgebra of a poset product of MV-chains and product chains with respect toa poset which is a forest. Although this embedding provides a representationfor finite BL-algebras, some limitations arise from the infinite case. Moreover,in [1] there are easy examples of BL-chains are not representable in the sense of poset product.The aim of this communication is to examine some features of the poset product construction in the context of BL. We will first consider the restrictionsreferred above in order to introduce the notion of idempotent free BL-chain.Then, we will suggest some requirements that a BL-algebra should satisfy sothat it admit a representation as a poset product of idempotent free BL-chains.References[1] M. Busaniche and C. Gomez. Poset product and BL-chains. Submitted.[2] M. Busaniche and F. Montagna. Hájek?s logic BL and BL-algebras. In Handbook of Mathematical Fuzzy Logic, volume 1 of Studies in Logic, Mathematical Logic and Foundations, chapter V, pages 355?447. College Publications,London, 2011.[3] P. Jipsen and F. Montagna. The Blok-Ferreirim theorem for normal GBLalgebras and its applications. Algebra Universalis, 60:381?404, 2009.[4] P. Jipsen and F. Montagna. Embedding theorems for classes of GBLalgebras. Journal of Pure and Applied Algebra, 214:1559?1575, 2010.