Quasi-rings and congruences in the theory of orthomodular algebras
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.
scientific article; zbMATH DE number 1899972