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Construction of p o -groups with quasi-divisors theory

Jiří Močkoř — 2000

Czechoslovak Mathematical Journal

A method is presented making it possible to construct p o -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups H ( Δ , ℤ ) , where Δ are finitely atomic root systems. Some examples of these constructions are presented.

Extensional subobjects in categories of Ω -fuzzy sets

Jiří Močkoř — 2007

Czechoslovak Mathematical Journal

Two categories 𝕊𝕖𝕥 ( Ω ) and 𝕊𝕖𝕥𝔽 ( Ω ) of fuzzy sets over an M V -algebra Ω are investigated. Full subcategories of these categories are introduced consisting of objects ( s u b ( A , δ ) , σ ) , where s u b ( A , δ ) is a subset of all extensional subobjects of an object ( A , δ ) . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

Complete subobjects of fuzzy sets over M V -algebras

Jiří Močkoř — 2004

Czechoslovak Mathematical Journal

A subobjects structure of the category Ω - of Ω -fuzzy sets over a complete M V -algebra Ω = ( L , ∧ , ∨ , ⊗ , → ) is investigated, where an Ω -fuzzy set is a pair 𝐀 = ( A , δ ) such that A is a set and δ A × A → Ω is a special map. Special subobjects (called complete) of an Ω -fuzzy set 𝐀 which can be identified with some characteristic morphisms 𝐀 → Ω * = ( L × L , μ ) are then investigated. It is proved that some truth-valued morphisms ¬ Ω Ω * → Ω * , ∩ Ω , ∪ Ω Ω * × Ω * → Ω * are characteristic morphisms of complete subobjects.

Topological characterizations of ordered groups with quasi-divisor theory

Jiří Močkoř — 2002

Czechoslovak Mathematical Journal

For an order embedding G → h → Γ of a partly ordered group G into an l -group Γ a topology 𝒯 W ^ is introduced on Γ which is defined by a family of valuations W on G . Some density properties of sets h ( G ) , h ( X t ) and ( h ( X t ) ∖ { h ( g 1 ) , ⋯ , h ( g n ) } ) ( X t being t -ideals in G ) in the topological space ( Γ , 𝒯 W ^ ) are then investigated, each of them being equivalent to the statement that h is a strong theory of quasi-divisors.

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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