# Proatomic modular ortholattices: representation and equational theory

@article{Herrmann2015ProatomicMO, title={Proatomic modular ortholattices: representation and equational theory}, author={Christian Herrmann and Michael S. Roddy}, journal={arXiv: Rings and Algebras}, year={2015} }

We study modular ortholattices in the variety generated by the finite dimensional ones from an equational and geometric point of view. We relate this to coordinatization results.

## 5 Citations

Linear representations of regular rings and complemented modular lattices with involution

- Mathematics
- 2015

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In…

On geometric representations of modular ortholattices

- Mathematics
- 2014

A pre-orthogonality on a projective geometry is a symmetric binary relation, ⊥, such that for each point $${p, p^{\perp} = \{q | p \perp q \}}$$p,p⊥={q|p⊥q} is a subspace. An orthogonality is a…

On linear representation of $\ast$-regular rings having representable ortholattice of projections.

- Mathematics
- 2018

This paper aims at the following results: \begin{enumerate} \item The class of all $*$-regular rings forms a variety. \item A subdirectly irreducible
$*$-regular ring $R$
is faithfully…

On varieties of modular ortholattices that are generated by their finite-dimensional members

- Mathematics
- 2014

AbstractWe prove that the following three conditions on a modular ortholattice L with respect to a given variety of modular ortholattices, $${\mathcal{V}}$$V, are equivalent: L is in the variety of…

A Note on the "Third Life of Quantum Logic"

- Philosophy
- 2019

The purpose of this note is to discuss some of the questions raised by Dunn, J. Michael; Moss, Lawrence S.; Wang, Zhenghan in Editors' introduction: the third life of quantum logic: quantum logic…

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