Equational theory of regular rings with involution and complemented modular polarity lattices
by
Christian Herrmann
Technische Universitaet Darmstadt
Coauthors: Florence Micol, Michael Roddy

Universal algebraic points of view have contributed to the understanding of the relationship between *-regular rings, modular ortholattices, and spaces with an anisotropic form. Yet, the main question remained unsolved in three equivalent versions: Is the variety of modular ortholattices generated by its finite dimensional members? Is every subdirectly irreducible *-regular ring a *-ring of operators? Is the free *-regular ring residually artinian? In the more general framework of regular rings with involution, orthogonal geometries, and polarity lattices these questions become more easily accessible - and contribute to the understanding of forms in general.

Date received: December 31, 2001