142 research outputs found
The rank of variants of nilpotent pseudovarieties
We investigate the rank of pseudovarieties defined by several of the variants
of nilpotency conditions for semigroups in the sense of Mal'cev. For several of
them, we provide finite bases of pseudoidentities. We also show that the
Neumann-Taylor variant does not have finite rank.Comment: 41 page
On Residually Finite Semigroups of Cellullar Automata
We prove that if is a monoid and a finite set with more than one
element, then the residual finiteness of is equivalent to that of the
monoid consisting of all cellular automata over with alphabet
Self-Automaton Semigroups
After reviewing automaton semigroups, we introduce Cayley Automata and the
corresponding Cayley Automaton semigroups. We investigate which semigroups are
isomorphic to their Cayley Automaton semigroup and give some results for
special classes of semigroups. We answer a question posed by Cain relating to
the dual construction.Comment: 18 page
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