Direct finiteness of representable regular rings with involution: A counterexample

2024/08/29 by Herrmann, Christian
#16E50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2408.16437

Abstract

Bruns and Roddy constructed a 3-generated modular ortholattice L which cannot be embedded into any complete modular ortholattice. Motivated by their approach, we use shift operators to construct a *-regular *-ring R of endomorphisms of an inner product space (which can be chosen as the Hilbert space ℓ²) such that direct finiteness fails for R.

Related

• Direct finiteness of representable regular rings with involution
• On linear representation of ∗-regular rings having representable ortholattice of projections
• Linear representations of regular rings and complemented modular lattices with involution
• Representations of *-regular rings and their ortholattices of projections
• Regularity and finite injective dimension in characteristic p>0