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Some properties of epimorphisms of Hilbert algebras

Dumitru Buşneag, Mircea Ghiţă (2010)

Open Mathematics

This paper represents a start in the study of epimorphisms in some categories of Hilbert algebras. Even if we give a complete characterization for such epimorphisms only for implication algebras, the following results will make possible the construction of some examples of epimorphisms which are not surjective functions. Also, we will show that the study of epimorphisms of Hilbert algebras is equivalent with the study of epimorphisms of Hertz algebras.

Some properties of Lorenzen ideal systems

Aleka Kalapodi, Angeliki Kontolatou, Jiří Močkoř (2000)

Archivum Mathematicum

Let G be a partially ordered abelian group ( p o -group). The construction of the Lorenzen ideal r a -system in G is investigated and the functorial properties of this construction with respect to the semigroup ( R ( G ) , , ) of all r -ideal systems defined on G are derived, where for r , s R ( G ) and a lower bounded subset X G , X r s = X r X s . It is proved that Lorenzen construction is the natural transformation between two functors from the category of p o -groups with special morphisms into the category of abelian ordered semigroups.

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