On a new construction of pseudo BL-algebras. (English) Zbl 1374.06021
Summary: We present a new construction of a class of pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop. Using two injective mappings from one set into the second one, and an identical copy of the basic pseudo hoop with the reverse order we construct a pseudo BL-algebra. We show that such a structure is a pseudo BL-algebra iff the basic pseudo hoop is cancellative. Starting with a commutative hoop we can obtain even a non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with non-commuting negations. We describe the construction, subdirect irreducible kite pseudo BL-algebras and their classification.
MSC:
| 06D35 | MV-algebras |
Keywords:
pseudo BL-algebra; pseudo hoop; basic pseudo hoop; \(\ell\)-group; kite pseudo BL-algebra; cancellativity; subdirect irreducibilitySoftware:
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