Aglianò-Montagna type decomposition of linear pseudo hoops and its applications (Q995635)

It was shown by \textit{A. Di Nola, F. Esteva, L. Godo} and \textit{F. Montagna} [Soft Comput. 9, No. 12, 875--888 (2005; Zbl 1092.03036)] that every linearly ordered pseudohoop can be represented as an ordinal sum of linear Wajsberg hoops. This result is extended in the paper under review to linear pseudohoops (even pseudo-BL-algebras) and linear pseudo-Wajsberg hoops. Using decompositions of the same type, the author (i) gives a new proof of his theorem [Soft Comput. 11, No. 6, 495--501 (2007; Zbl 1122.06012)] stating that every representable pseudo-BL-algebra is good, i.e., the two negations commute in it, (ii) proves that every \(\sigma\)-complete linear pseudohoop is commutative, (iii) shows that every maximal filter and every value of a linear pseudohoop is normal.