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On reductive and distributive algebras

Anna B. Romanowska (1999)

Commentationes Mathematicae Universitatis Carolinae

The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left k -step reductive Ω -algebras, and of right n -step reductive Ω -algebras, are independent for any positive integers k and n . This gives a structural description of algebras in the join of...

On some non-obvious connections between graphs and unary partial algebras

Konrad Pióro (2000)

Czechoslovak Mathematical Journal

In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras 𝐀 and 𝐁 , their weak subalgebra lattices are isomorphic if and only...

On the special context of independent sets

Vladimír Slezák (2001)

Discussiones Mathematicae - General Algebra and Applications

In this paper the context of independent sets J L p is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions

Hans-Jürgen Vogel (2001)

Discussiones Mathematicae - General Algebra and Applications

The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family d = ( d A : A → A ⨂ A | A ∈ | R e l | ) of diagonal morphisms, a family t = ( t A : A → I | A ∈ | R e l | ) of terminal morphisms, and a family ∇ = ( ∇ A : A ⨂ A → A | A ∈ | R e l | ) of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....

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