4 research outputs found
On Normal-Valued Basic Pseudo Hoops
We show that every pseudo hoop satisfies the Riesz Decomposition Property. We
visualize basic pseudo hoops by functions on a linearly ordered set. Finally,
we study normal-valued basic pseudo hoops giving a countable base of equations
for them
Filters on some classes of quantum B-algebras
In this paper, we continue the study of quantum B-algebras with emphasis on
filters on integral quantum B-algebras. We then study filters in the setting of
pseudo-hoops. First, we establish an embedding of a cartesion product of polars
of a pseudo-hoop into itself. Second, we give sufficient conditions for a
pseudohoop to be subdirectly reducible. We also extend the result of Kondo and
Turunen to the setting of noncommutative residuated -semilattices that,
if prime filters and -prime filters of a residuated -semilattice
coincide, then must be a pseudo MTL-algebra
On pseudo BL-algebras and pseudo hoops with normal maximal filters
We study the class of pseudo BL-algebras whose every maximal filter is
normal. We present an equational base for this class and we extend these
results for the class of basic pseudo hoops with fixed strong unit
Kites and Pseudo BL-algebras
We investigate a construction of a pseudo BL-algebra out of an -group
called a kite. We show that many well-known examples of algebras related to
fuzzy logics can be obtained in that way. We describe subdirectly irreducible
kites. As another application, we exhibit a new countably infinite family of
varieties of pseudo BL-algebras covering the variety of Boolean algebras