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Abstract orthogonality and orthocomplementation

Published online by Cambridge University Press:  24 October 2008

Gianpiero Cattaneo  and
Alessandro Manià
Gianpiero Cattaneo
Affiliation:
Istituto di Scienze Fisiche dell'università, 20133 Milano, Italy
Alessandro Manià
Affiliation:
Istituto di Scienze Fisiche dell'università, 20133 Milano, Italy
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Abstract

The notion of orthogonality is axiomatically defined on a poset. Various notions of orthocomplementation are distinguished and conditions are given in order to induce an orthocomplementation from an orthogonality and vice versa. Subsequently ⊥-modular ⊥-poset are defined and the set of morphisms between two posets with orthogonality is briefly discussed. Given the notions of additive monoid and of positive semi-ring, an orthogonality relation is introduced on the set of idempotent elements of a positive semi-ring. Finally, the obtained results are applied to the set of idempotent and absorbent endomorphisms of an additive monoid.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 115 - 132
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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