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On decomposition of pseudo BL-algebras

In: Mathematica Slovaca, vol. 61, no. 3
Anatolij Dvurečenskij - O. Kowalski
Detaily:
Rok, strany: 2011, 307 - 326
Kľúčové slová:
pseudo MV-algebra, pseudo BL-algebra, pseudo hoop, idempotent, $\ell$-group, unital $\ell$-group, Wajsberg algebra
O článku:
We show that under some conditions, imposed on coatoms and maximal idempotents of a pseudo BL-algebra, we can decompose a pseudo BL-algebra $M$ as an ordinal sum and we show that then $M$ is linearly ordered. We investigate pseudo BL-algebras with a unique coatom $a$ and with a maximal idempotent, and analyze two main situations: either $an=an+1$ holds for some $n≥ 1$, or $an > an+1$ hold for any $n≥ 1$. We note that there exist (subdirectly irreducible) algebras with two coatoms that are not linearly ordered, so the restriction to a single coatom is natural.
Ako citovať:
ISO 690:
Dvurečenskij, A., Kowalski, O. 2011. On decomposition of pseudo BL-algebras. In Mathematica Slovaca, vol. 61, no.3, pp. 307-326. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0014-5

APA:
Dvurečenskij, A., Kowalski, O. (2011). On decomposition of pseudo BL-algebras. Mathematica Slovaca, 61(3), 307-326. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0014-5
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