Monoids Respectingn-Chains of Intervals Original Research Article

A new strict hierarchy for the pseudovariety of aperiodic monoids is described. Thenth level of the hierarchy is the pseudovariety of all divisors of monoids of full transformations of finite chains respecting somen-chain of intervals. The levels can be obtained by iterated semidirect product of the first level. The associated hierarchy corresponding to taking partial transformations is also considered and appears intermingled with the above hierarchy.