Christian Herrmann

collaborators

6 papers

math.LO2025

Some remarks on lattices of equivalences

Christian Herrmann

We review principal results on axiomatizability of classes of lattices of equivalences

math.LO2025

On the equational theory of finite modular lattices

Christian Herrmann

It is shown that there is $N$ such that there is no algorithm to decide for identities in at most $N$ variables validity in the class of finite modular lattices. This is based on S…

math.RA2025

Perspectivity in complemented modular lattices and regular rings

Christian Herrmann

Based on an analogue for systems of partial isomorphisms between lower sections in a complemented modular lattice we prove that principal right ideals $a R ≅ b R$ in a (von Neuma…

math.CO2024

S-Glued sums of lattices

Christian Herrmann, Dale R. Worley

For many equation-theoretical questions about modular lattices, Hall and Dilworth give a useful construction: Let $L_{0}$ be a lattice with largest element $u_{0}$ , $L_{1}$ be a lattice…

math.RA2024

Unit-regularity and representability for semiartinian *-regular rings

Christian Herrmann

We show that any semiartinian subdirectly irreducible *-regular ring R admits a representation within some inner product space.

math.RA2024

Direct finiteness of representable regular rings with involution: A counterexample

Christian Herrmann

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 oper…