Agliano-Montagna type decomposition of linear pseudo hoops and its applications

We decompose every linear pseudo hoop as an Agliano-Montagna type of ordinal sum of linear Wajsberg pseudo hoops which are either negative cones of linear l-groups or intervals in linear unital l-groups with strong unit. We apply the decomposition to present a new proof that every linear pseudo BL-algebra and consequently every representable pseudo BL-algebra is good. Moreover, we show that every maximal filter and every value of a linear pseudo hoop is normal, and every a-complete linear pseudo hoop is commutative. (c) 2007 Elsevier B.V. All rights reserved.