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Binary and ternary relations

Vítězslav Novák, Miroslav Novotný (1992)

Mathematica Bohemica

Two operators are constructed which make it possible to transform ternary relations into binary relations defined on binary relations and vice versa. A possible graphical representation of ternary relations is described.

Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations

Stanisław Kasjan (1993)

Fundamenta Mathematicae

A class of stratified posets I * ϱ is investigated and their incidence algebras K I * ϱ are studied in connection with a class of non-shurian vector space categories. Under some assumptions on I * ϱ we associate with I * ϱ a bound quiver (Q, Ω) in such a way that K I * ϱ K ( Q , Ω ) . We show that the fundamental group of (Q, Ω) is the free group with two free generators if I * ϱ is rib-convex. In this case the universal Galois covering of (Q, Ω) is described. If in addition I ϱ is three-partite a fundamental domain I * + × of this covering is...

Bourbaki's Fixpoint Lemma reconsidered

Bernhard Banaschewski (1992)

Commentationes Mathematicae Universitatis Carolinae

A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L . This is then used to deal with coproducts and other aspects of frames.

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