On linear representation of ∗-regular rings having representable ortholattice of projections

2018/11/04 by Herrmann, Christian, Niemann, Niklas
#06C20 #16E50 #16W10 #51D #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1811.01392

Abstract

This paper aims at the following results: \beginenumerate \item The class of all *-regular rings forms a variety. \item A subdirectly irreducible *-regular ring R is faithfully representable (i.e. isomorphic to a subring of an endomorphisms ring of vector spaces, where the involution is given by adjunction with respect to a scalar product on the vector space) if so is its ortholattice of projections. \endenumerate This is a short version of the second author's PhD thesis.

Related

• Representations of *-regular rings and their ortholattices of projections
• Linear representations of regular rings and complemented modular lattices with involution
• Direct finiteness of representable regular rings with involution: A counterexample
• Unit-regularity and representability for semiartinian *-regular rings
• Direct finiteness of representable regular rings with involution