Iteration of expansions — unambiguous semigroups

摘要: New expansions for global semigroup theory are developed. Many have a left and right version, each with specific (dual) properties; e.g., the Rhodes ŜL, resp. ŜR, unambiguous L-resp. R-order. In applications one sometimes needs having both properties simultaneously; these can be constructed by alternately applying expansion (possibly infinitely often) while keeping same set of generators. Thus obtains an which is invariant under application old two thus has (e.g., -+ , so L-and R-order). It proved that, in case expansion, new ‘close’ to original semigroup; particular (and this main result paper), Ŝ+A finite (resp. J-above) if S finiteJ-above).