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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...

Bounded lattices with antitone involutions and properties of MV-algebras

Ivan Chajda, Peter Emanovský (2004)

Discussiones Mathematicae - General Algebra and Applications

We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by...

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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