Commutative ring
Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
... The zero-divisor graph of a commutative ring has also been studied by several other authors. The zero-divisor graph has also been introduced for semigroups and other algebraic structures. There are a lot of ...
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The compressed annihilator graph of a commutative ring
... The annihilator graph AG(R) for a commutative ring R was introduced and investigated by Badawi in [5]. Let a ∈ Z(R) and let ann(a) = {r ∈ R|ra = 0}. AG(R) is the graph with vertices Z (R) ∗ , and two ...
10
A graph associated to spectrum of a commutative ring
... commutative ring. There are many papers on assigning a graph to a ring, see for example [4], [3], [5], [7] and ...arbitrary commutative ring R, we define the Spec-graph of R, which is ...
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On the genus of the annhilator graph of a commutative ring
... a commutative ring R, the zero-divisor graph is the simple graph with R as the vertex set and two distinct elements x and y are adjacent if and only if xy = 0 ...
18
Properties of extended ideal based zero divisor graph of a commutative ring
... a commutative ring with identity. The zero divisor graph of a ring R, denoted by Γ(R), is the simple graph associated to R such that its vertex set consists of all its nonzero divisors and that two ...
5
On modules over group rings of soluble groups with commutative ring of scalars
... cocentralizers in the module A are not Noetherian R -modules or simply that the group G satisfies the condition max − nnd. In this paper we study soluble groups with the condition max − nnd and generalize the results on ...
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A variant of the primitive element theorem for separable extensions of a commutative ring
... a commutative ring 𝑅 can be embedded into another one having primitive element whenever every boolean lo- calization of 𝑅 modulo its Jacobson radical is von Neumann regular and locally ...
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Generalization of Schur's Lemma in Ring Representations on Modules over a Commutative Ring
... of ring on the module over a commutative ring, the generalization of Schur’s Lemma is ...a ring R depend on the properties of a ring S and M as ...
11
The k Zero Divisor Hypergraph of a Commutative Ring
... a commutative ring has been studied by many authors, and the k-zero-divisor hypergraph of a commutative ring is a nice abstraction of this ...a commutative ring and k an integer ...
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Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case
... a ring has begun with the work of Chakrabarthy, Ghosh, Mukherjee and Sen ...a ring with identity which is not necessarily ...the ring of integers modulo n by Z n ...characterized commutative ...
14
Some results on a subgraph of the intersection graph of ideals of a commutative ring
... are commutative with identity which admit at least one nonzero proper ...a ring with identity which is not necessar- ily commutative and which admits at least one nonzero left ideal I with I 6= ...
27
An outer measure on a commutative ring
... In the paper, we will show that an arbitrary measure on a suitable subfamily of Spec( R ) induces an outer measure on R with good multi- plicative properties.. We will also discuss a few[r] ...
8
Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case
... the ring R plays a role in arriving at the conclusion that H(R) is planar if H(R) satisfies at least one between (C 1 ) and (C 2 ), where for each i ∈ {1, 2}, ...
27
A Note on a graph associated to a commutative ring
... We now give a brief summary of the results that are proved in Section 2 of this article. Let R be a ring. It is observed in Lemma 2.1 that Γ(R) is a spanning subgraph of G(R). It is noted in Lemma 2.2 that G(R) is ...
22
Number theoretic properties of the commutative ring Zn
... Here, we present a program in C-language for finding the sets of all non-unit elements in 𝑍 𝑛 whose principal ideals are equally generated in 𝑍 𝑛 along with th[r] ...
12
More on the Schur group of a commutative ring
... generalized to the ring case, viz: If G is a finite group of exponent m, and R is a connected ring with RG being separable then R[em] is a splitting ring for G; i.e... Azumaya algebras w[r] ...
8
Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences
... A-module. By [18, 3.3], the complex of modules of generalized fractions C( U , M) is exact if and only if, for each i ∈ N , each member of U i is a poor M -sequence. (Although the present second author and H. Zakeri ...
11
Unstable K cohomology algebra is filtered λ ring
... which induce the natural addition (by µ) and multiplication (by φ) structure on the K-theory K(X) of a space X. These maps satisfy certain associativity, commutativity, and so on, conditions which make K(X) a ...
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Exact annihilating-ideal graph of commutative rings
... Proof. Let R be a commutative ring such that the exact annihilating- ideal graph EAG(R) of R is connected. Suppose that the length of the shortest path between any two vertices is bigger than two. Thus let ...
7
Ring Homomorphic Encryption Schemes
... finite commutative rings and their associated idempotent ...finite ring to its idempotent ...of commutative ring homomorphic encryption schemes. If R is a ring then we denote by E(R) ...
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