Class of algebras of primitive recursive functions

In this paper Robinson's algebra is embedded in a countable class of algebras of primitive recursive functions. Each algebra of this class contains the operations of addition and composition of functions and also one of the operations i_a which are defined as follows: g(x)= i _a f(x) (a=0, 1, 2, ...) if g(x) satisfies the equations g(0)=a and g(x+1)=fg(x)]. In this paper we study the properties possessed by all or almost all the algebras of this class.Translated from Matematicheskie Zametki, Vol. 14, No. 1, pp. 143–156, July, 1973.