Universal Algebra Seminar

Matthew Moore, Vanderbilt University

“Absorption and directed Jonsson terms”

We prove that every congruence distributive (CD) variety has directed Jonsson terms, and every congruence modular (CM) variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original Jonsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in CD and CM varieties, respectively. For finite algebras, these absorption theorems have already seen significant applications, but until now, it was not clear if the theorems hold for general algebras as well.

MC 5403