On clones, transformation monoids, and associative rings (Q1272131)

The author studies a partition of the clone lattice Lat\(A\) on a finite set \(A\), \(| A | \geq 3\). Each class of this partition consists of all clones having the same set of unary functions and forms an interval in Lat\(A\). These intervals are called monoidal. Intervals determined by monoids of all linear functions over a finite associative ring with unit are investigated. The author solves a problem of \textit{Á. Szendrei} by finding three classes of monoids such that the corresponding monoidal intervals are (i) finite; (ii) countable; (iii) uncountable.