Lattices allowing only nilpotent commutator operations
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
AAA93 - 93. Arbeitstagung Allgemeine Algebra - 93rd workshop on general algebra
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
Expanding the congruence lattice $\mathbb{L}$ of an algebra with the binary
commutator operation, we obtain a new algebraic structure
\[ \mathbf{L} = (\mathbb{L}, \vee, \wedge, [.,.]); \]
such a structure has been called a \emph{commutator lattice}
by J.\ Czelakowski, and $[.,.]$ a \emph{commutator multiplication}
on $\mathbb{L}$.
We characterize those modular lattices of finite height on which
every such commutator multiplication is ``nilpotent''.
The main task here is to construct non-nilpotent multiplications
on certain modular lattices. <a href="http://www.algebra.uni-linz.ac.at/Slides/slides-aaa93-aichinger-v2.pdf">Slides</a>.