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Products in almost f -algebras

Karim Boulabiar (2000)

Commentationes Mathematicae Universitatis Carolinae

Let A be a uniformly complete almost f -algebra and a natural number p { 3 , 4 , } . Then Π p ( A ) = { a 1 a p ; a k A , k = 1 , , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 a A } as positive cone.

Products of partially ordered quasigroups

Milan Demko (2008)

Commentationes Mathematicae Universitatis Carolinae

We describe necessary and sufficient conditions for a direct product and a lexicographic product of partially ordered quasigroups to be a positive quasigroup. Analogous questions for Riesz quasigroups are studied.

Projectability and weak homogeneity of pseudo effect algebras

Ján Jakubík (2009)

Czechoslovak Mathematical Journal

In this paper we deal with a pseudo effect algebra 𝒜 possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, 𝒜 can be represented as an interval of a unital partially ordered group G . We prove that 𝒜 is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of 𝒜 and of G is shown to be valid.

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