The Basic Properties of SCM over Ring
نویسنده
چکیده
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
منابع مشابه
NILPOTENT GRAPHS OF MATRIX ALGEBRAS
Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...
متن کاملThe Properties of Instructions of SCM over Ring
The papers [16], [9], [11], [12], [15], [19], [2], [3], [5], [6], [4], [1], [20], [21], [17], [8], [7], [13], [18], [14], and [10] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: R denotes a good ring, r denotes an element of the carrier of R, a, b denote Data-Locations of R, i1, i2, i3 denote instruction-locations of SCM(R), I denotes an ...
متن کاملUniformly Secondary Modules over Commutative Ring
In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.
متن کاملEnhancing Basic Metal Industry Global Competitiveness Through Total Quality Management, Supply Chain Management & Just- In -Time
The selection and implantation of sufficient and appropriate continuous improvement strategy are the key success factors for improving firm performance and enhancement of competitive advantage on manufacturing industries. As a result special role are given to Continuous improvement programs such as Supply Chain Management (SCM), Six-Sigma, Total Quality Management (TQM), Kaizen, Just-in-Time (J...
متن کاملCLASSICAL 2-ABSORBING SECONDARY SUBMODULES
In this work, we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules. Let $R$ be a commutative ring with identity. We say that a non-zero submodule $N$ of an $R$-module $M$ is a emph{classical 2-absorbing secondary submodule} of $M$ ...
متن کامل