# ALGEBRAS OF UNARY OPERATIONS OF RANG 3.

This work is devoted to finding all algebras of unary operations of rank 3. This question is relevant, since the algebras of operations and multioperations are used in the theory of the synthesis of discrete information converters. The paper presents a new method for describing algebras of operations through multioperations using the semipermutability identity and the Galois connection. The first section contains definitions of operations, multioperations, superposition operations and multioperations, semi-commutative identities, algebra of operations and multioperations. The second section of the paper describes the finding of algebras of unary operations of rank 3 using the semipermutability identity and the Galois connection. The search for algebras of unary operations of rank 3 was implemented in Python. The result obtained using the method of describing algebras of operations through multioperations coincided with the already available results presented in the work of Lay D. «Functional algebras on finite sets». As a result, using the Galois connection, all algebras of unary operations of rank 3 were described via binary multioperations.

**Authors:** D. A. Eremenko

**Direction:** Informatics, Computer Technologies And Control

**Keywords:** Multioperations, semi-permutability identities, operations, algebras of unary operations

View full article