On representability of *-regular rings and modular ortholattices [Elektronische Ressource] / von Florence Micol

On representabilityof-regular ringsand modular ortholatticesVom Fachbereich Mathematikder Technischen Universit at Darmstadtzur Erlangung des Grades einerDoktorin der Naturwissenschaften(Dr. rer. nat)genehmigte DissertationvonDipl.-Math. Florence Micolaus Saint-EtienneReferent: Prof. Dr. Chr. HerrmannKorreferent: Prof. Dr. K. H. NeebTag der Einreichung: 9. Januar 2003Tag der mundlic hen Prufung: 31. Januar 2003Darmstadt 2003D17In this thesis a proof is given that simple modular ortholattices possessing achain with at least ve elements (or four if they are arguesian) are coordi-natizable by a-regular ring also with respect to the orthocomplementation.This is based on the fact that their lattice reduct possesses a large partialthree-frame and hence satis es a stricter condition of coordinatization yield-ing the involution on the coordinatizing ring. Simple modular ortholatticesplay an important role in the equational theory of modular ortholattices,since any variety of modular ortholattices is generated by its simple mem-bers, as shown by Herrmann and Roddy.As a second main result, a characterization of the smallest classV of-regular rings containing the classA of artinian-regular rings and closedunder homomorphic images (H), products (P ) and regular substructures(S ) is set up. In fact, the elements ofV are exactly the-regular ringsrthat can be embedded into an atomic-regular ring, resp.