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Displaying similar documents to “The algebra of mode homomorphisms”

Embedding sums of cancellative modes into semimodules

Anna B. Romanowska, Anna Zamojska-Dzienio (2005)

Czechoslovak Mathematical Journal

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A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.

Representation of Hilbert algebras and implicative semilattices

Sergio Celani (2003)

Open Mathematics

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In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.

Hilbert algebras as implicative partial semilattices

Jānis Cīrulis (2007)

Open Mathematics

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The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice...