Algebras Related to Logic (BCK /BCI-algebras, Hilbert algebras, implication algebras) Research Papers (original) (raw)

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On the ordered algebraic structure of Hilbert algebras (spanish). M.Sc. Thesis

• • by Aldo Figallo Orellano
  • •
  • Algebraic Logic, Algebras Related to Logic (BCK /BCI-algebras, Hilbert algebras, implication algebras)

In [6], iH-algebras were introduced in order to indicate an equational version of the class of Hilbert algebras where each pair of elements has infimum. These authors also proved that this variety has the class of Curry’s implicative... more

In [6], iH-algebras were introduced in order to indicate an equational version of the class of Hilbert algebras where
each pair of elements has infimum. These authors also proved that this variety has the class of Curry’s implicative
semilattices ([9]) as a proper subvariety. On the other hand, in [4] a special class of Hilbert algebras associated with
ordered sets, which they called order algebras, were investigated. These algebras were also studied in [1] under the
name of pure Hilbert algebras.
Bearing in mind the above results, in this paper we introduce the notion of pure Hilbert algebras with infimum
(or ipH-algebras, for short). Furthermore, we characterize the lattice of ipH-congruences and we determine the
subdirectly irreducibleipH-algebras. Besides, we prove that subdirectly irreducibleipH-algebras are also subdirectly
irreducible iH-algebras

• • by Aldo Figallo Orellano
  • •
  • Logic, Algebraic Logic, Algebras Related to Logic (BCK /BCI-algebras, Hilbert algebras, implication algebras)