Congruences on monoids of transformations preserving the orientation on a finite chain.
The authors consider the following monoids of transformations on a finite chain: the monoid of all transformations preserving or reversing the orientation; the monoid of all partial transformations preserving or reversing the orientation; the monoid of all transformations preserving the orientation; the monoid of all partial transformations preserving the orientation; and the intersection of the two monoids of partial transformations mentioned above with the symmetric inverse semigroup. For these monoids the authors describe Green's relations and show that any congruence can be obtained basically in the same way as for the full transformation semigroup, as described by \textit{A. I. Mal'tsev} [in Mat. Sb., N. Ser. 31(73), 136-151 (1952; Zbl 0048.25204), English translation in Am. Math. Soc., Translat., II. Ser. 113, 235-250 (1979)]. Unfortunately, in their historical overview the authors do not mention the above paper at all. They also do not mention many similar results for other classical transformation semigroups obtained by several other people. More complete information can be found for example in Chapter 6 of \textit{O. Ganyushkin} and \textit{V. Mazorchuk} [Classical finite transformation semigroups. An introduction. Algebra Appl. 9. London: Springer (2009; Zbl 1166.20056)].
scientific article; zbMATH DE number 5549333