2 research outputs found
Independence of algebras with edge term
Two varieties of the same type are independent if there is a binary
term such that and . In this note, we give necessary and sufficient conditions for two
finite algebras with a Mal'cev term (or, more generally, with an edge term) to
generate independent varieties. In particular we show that the independence of
finitely generated varieties with edge term can be decided by a polynomial time
algorithm
Two-sided wreath product done right
We investigate a semigroup construction related to the two-sided wreath
product. It encompasses a range of known constructions and gives a slightly
finer version of the decomposition in the Krohn-Rhodes Theorem, in which the
three-element flip-flop is replaced by the two-element semilattice. We develop
foundations of the theory of our construction, showing in the process that it
naturally combines ideas from semigroup theory (wreath products), category
theory (Grothendieck construction), and ordered structures (residuated
lattices)