Basic Concepts of Difference Algebra

In what follows we keep the basic notation and conventions of Chapter 1. In particular, by a ring we always mean an associative ring with unity, every ring homomorphism is unitary (maps unity onto unity), every subring of a ring contains the unity of the ring. Unless otherwise indicated, by the module over a ring A we mean a left A-module. Every module over a ring is unitary and every algebra over a commutative ring is also unitary.