Boolean perspectives of idioms and the Boyle derivative
Abstract
We are concerned with the boolean or more general with the complemented properties of idioms (complete upper-continuous modular lattices). In [Simmons&Cantor] the author introduces a device which captures in some informal speaking how far the idiom is from be complemented, this device is the Cantor-Bendixson derivative. There exists another device that captures some boolean properties, the so-called Boyle-derivative, this derivative is an operator on the assembly (the frame of nuclei) of the idiom. The Boyle-derivative has its origins in module theory. In this investigation we produce an idiomatic analysis of the boolean properties of any idiom using the Boyle-derivative, we give conditions on a nucleus such that is a complete boolean algebra. We also explore some properties of nuclei such that is a complemented idiom.
Keywords
Cite
@article{arxiv.1708.02619,
title = {Boolean perspectives of idioms and the Boyle derivative},
author = {Jaime Castro Pérez and Mauricio Medina Bárcenas and José Ríos Montes and Ángel Zaldívar},
journal= {arXiv preprint arXiv:1708.02619},
year = {2017}
}