Quasi-rings and congruences in the theory of orthomodular algebras
type: Item
instance of: scholarly article
title: Quasi-rings and congruences in the theory of orthomodular algebras
zbMATH Open document ID: 1013.08006
author: Peter Burmeister
author: Richard Holzer
author: Maciej Mączyński
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: The concept of an orthomodular (partial) algebra (briefly OMA) was introduced by the first author in 1994. In this paper, the theory of OMAs is further developed. The concept of a Boolean quasi-ring, introduced by the last author together with H. Länger and D. Dorninger, is extended to the partial case. The connection of quasi-rings with the structure of OMAs is investigated. It is shown that OMAs can be defined equivalently as the so-called compatible partial orthomodular quasi-rings. Further, the authors investigate the ordered set of all OMA-congruences (i.e. those congruences for which the factor algebra is again an OMA). These congruences are characterized by axioms and compared with another concept of congruences introduced by S. Pulmannová with the so-called OMA-Schmidt congruences.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A55
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 1899972
zbMATH Keywords: orthomodular algebras
zbMATH Keywords: quasi-rings
zbMATH Keywords: Schmidt congruences
MaRDI profile type: Publication
full work available at URL: s000120050192
OpenAlex ID: W2081015770
DOI: 10.1007/S000120050192
description: scientific article; zbMATH DE number 1899972