3 papers
math.LO2017
Closure operators on dcpos
France Dacar
We examine collective properties of closure operators on posets that are at least dcpos. The first theorem sets the tone of the paper: it tells how a set of preclosure maps on a dc…
math.RA2014
Quadratic Extension Algebras and Quaternion Algebras Over Fields (of Characteristic not 2)
France Dacar
The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (o…
math.NT2013
Euclidean quadratic forms are ADC forms: A short proof
France Dacar
This note presents a short, transparent proof of the theorem that every Euclidean quadratic form over a normed integral domain is an Aubry-Davenport-Cassels form. The theorem, as f…