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The Basic Properties of SCM over Ring

In this paper I is an element of Z8, S is a non empty 1-sorted structure, t is an element of the carrier of S, and x is a set. Let R be a good ring. The functor SCM(R) yields a strict AMI over {the carrier of R} and is defined by the conditions (Def. 1). (Def. 1)(i) The objects of SCM(R) = N, (ii) the instruction counter of SCM(R) = 0, (iii) the instruction locations of SCM(R) = Instr-LocSCM, (iv) the instruction codes of SCM(R) = Z8, (v) the instructions of SCM(R) = InstrSCM(R), (vi) the object kind of SCM(R) = OKSCM(R), and (vii) the execution of SCM(R) = ExecSCM(R). Let R be a good ring, let s be a state of SCM(R), and let a be an element of Data-LocSCM. Then s(a) is an element of R. Let R be a good ring. An object of SCM(R) is called a Data-Location of R if: (Def. 2) It ∈ (the objects of SCM(R)) \ (Instr-LocSCM ∪ {0}). For simplicity, we use the following convention: R is a good ring, r is an element of the carrier of R, a, b, c, d1, d2 are Data-Location of R, and i1 is an instruction-location of SCM(R). Next we state the proposition