This study is a continuation of Scientific Report No. 4. Irreducibility conditions for non-connected unary algebras are established. Irreducible representations of unary algebras are demonstrated to be non-unique and a computational method for obtaining an irreducible representation of an arbitrary basic algebra is derived. Furthermore, the concept of decomposability is introduced and related to that of reducibility. A unary algebra is decomposable if it can be non-trivially represented as the homomorphic image of a sub algebra of the direct product of two other unary algebras.
展开▼
