For a finite von Neumann algebra factor M, the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(ℂ n × n ) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂ n × n ) is shown to be undecidable.

ZusammenfassungDie wichtigsten Werke Edmund Schlinks zur ökumenischen Theologie erscheinen in einer Neuedition. Die im ersten Band enthaltenen Vorträge stellen heraus, dass Ökumene von Gott her empfangen wird. Der Mensch trägt in der Gestalt der Buße, durch die Überwindung theologischer Reduktionismen zur Ökumene bei.SummaryThe most important works of Edmund Schlink concerning the ecumenical theology will be published in a new edition. The lectures contained in the first volume of this edition emphasize: ecumene can be received by God. Man contributes to ecumene (...) by penance, by overcoming of theological reductionisms. (shrink)

Basic motor competencies are a prerequisite for children to be physically active, participate in sports and thus develop a healthy, active lifestyle. The present study provides a broad screening of BMC and associations with age, sex, body mass index and extracurricular physical activity in 10 different European countries. The different country and regional contexts within Europe will offer a novel view on already established BMC associations. The cross-sectional study was conducted in 11 regions in 10 European countries in 2018. The (...) motor competence areas, object movement and self-movement, were assessed using the MOBAK-1-2 test instrument in 3758 first and second graders during Physical Education classes. Children were questioned about their extracurricular PA and age. Their body weight and height were measured in order to calculate BMI. Statistical analyses included variances and correlations. The results showed significant differences in BMC levels between countries whereas associations between BMC and correlates were similar. Boys performed significantly better in OM while girls performed better in SM. Age was consistently positively related to OM and SM with older children reaching higher levels of BMC than younger ones. While participation rates for extracurricular PA differed widely, participation in ball sports was correlated with OM and SM. Participation in individual sports showed a significant association with SM. In summary, BMC levels of children seem to depend on where they live and are strongly related to their participation in extracurricular PA. Therefore, education and health policies, in order to enhance motor competence development and PA participation, are recommended. Further research on country-specific Physical Education frameworks and their influence on BMC will provide more insights into structural factors and cultural characteristics of BMC development. On a school level, support tools and educational materials for teachers about BMC may enable children to achieve a basic level of motor competencies through Physical Education, contributing to lifelong participation in PA. (shrink)