About one $SI^{\ast}$-interval of rank $2$ multioperations

I. V. Fomina^a, V. I. Panteleev<sup>ba

a</sup> Buryat State University, Ulan-Ude
^b Irkutsk State University

Abstract: We consider rank-$2$ multi-operations. The superposition is defined on the basis of a set-theoretic intersection operation with selection of a single element. The interval between the clone of self-transitive operations and the multiclone of all multi-operations is described. The results obtained can be applied to the description of other intervals in the lattice of rank-$2$multiclones.

Keywords: interval, multioperation, superposition, clone, closed set

UDC: 519.716

MSC: 08A99

DOI: 10.36535/2782-4438-2025-241-71-82