The uniqueness theorem for finite φ- representations of algebras

Abstract

In the present paper we consider φ-representations of algebras. (The concept of a φ-representation is denfined in [7] more generaly.) we characterize such representations in terms of congruence relations (see Theorems 1 and 2). The main result of our paper is a unique factorization theorem (cf. Theorem 3). This result implies some classical theorems on direct and subdirect products.