[PDF] Top 20 The k Zero Divisor Hypergraph of a Commutative Ring
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The k Zero Divisor Hypergraph of a Commutative Ring
... on zero-divisor graphs, the edges are defined to be between the distinct nonzero zero-divisors in order to construct a graph with no ...for k-zero-divisors in order to have a ... See full document
15
Finite generation of Hochschild cohomology of Hecke algebras of finite classical type in characteristic zero
... Let k be a commutative Noetherian ring and let A be a ...relatively k-injective if every A-homomorphism from U to another A-module V which is split injective as k-homomorphism, is split ... See full document
15
Zero divisor graphs of posets
... of zero divisor graphs over a non-commutative ...about zero divi- sor graphs of non-commutative rings, we have studied the zero divisor graphs of matrices over ... See full document
13
On the Cozero Divisor Graphs of Commutative Rings
... of zero-divisor graph of a commutative ring was introduced by Beck [1], but this work was mostly concerned with colorings of ...The zero-divisor graphs of commuta- tive rings ... See full document
7
The compressed annihilator graph of a commutative ring
... a commutative ring with non-zero identity, Z(R) its set of zero- divisors, Nil(R) its set of nilpotent elements, Ass(R) its set of associated primes and Min(R) its set of minimal prime ... See full document
10
On Commutativity of Rings Under Certain Polynomial Constraints
... a ring with unity 1 satisfying certain polynomial ...a ring is commutative if at least one of the integral exponent used in the polynomial constraints of the theorem is zero and the ... See full document
7
A generalization of zero-divisor graphs
... One of the interesting areas of research in algebraic combinatorics is to associate a graph G(A) to an algebraic structure A and investigate the interplay between the algebraic properties of the algebra A and the ... See full document
11
On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
... arbitrary ring R, the zero-divisor graph of R, denoted by Γ(R), is an undirected simple graph that its vertices are all nonzero zero-divisors of R in which any two vertices x and y are ... See full document
12
A NOTE ON LINE GRAPHS
... a commutative ring R, the notion of zero divisor graph is given in Beck ...be commutative) and we will provide some examples on the zero divisor graphs of Z n where n is a ... See full document
7
INDEPENDENCE AND CLIQUE POLYNOMIALS OF ZERO-DIVISOR GRAPH OF THE INTEGER MODULO n (ℤ𝒏)
... of zero-divisor graphs of the integers modulo ...the zero-divisor graphs of five commutative rings; ℤ 10 , ℤ 12 , ℤ 14 , ℤ 15 , ℤ 16 , ... See full document
17
Properties of extended ideal based zero divisor graph of a commutative ring
... extended zero divisor graph of R, such that its vertex set consists of all its nonzero zero divisors and that two distinct vertices x and y are joined by an edge if and only if there exists two non ... See full document
5
Several result on SD-prime cordial graphs
... to zero-divisors of a commutative ring was introduced by ...a commutative ring with non-zero identity, Z(R) its set of all zero-divisors in R and Z ∗ (R) = ...The ... See full document
7
On the genus of the k annihilating ideal hypergraph of commutative rings
... linking commutative ring theory with graph theory has been started with the concept of the zero-divisor graph of a commutative ...a commutative ring and Z(R) ∗ be the set ... See full document
15
Exact annihilating-ideal graph of commutative rings
... integers, ring of integers modulo n and field with m elements, re- ...of zero divisors and set of exact zero divisors of R, ...polynomial ring in one variable X over ... See full document
7
Associated Graphs of Modules Over Commutative Rings
... of zero-divisors of a commutative ring was introduced in [14], by studying the coloring of a graph constructed by all elements of a commutative ring ...the ring-theoretic ... See full document
14
Construction of Zero Divisor Graphs of Rings
... The zero-divisor graph was first introduced by Beck (1988)[1] in the study of commutative ...a ring 𝑅, 𝐺(𝑅) denote the graph whose vertex set is 𝑅, such that distinct vertices 𝑟 and 𝑠 are ... See full document
6
A Note on a graph associated to a commutative ring
... are commutative with ...any ring R, we associate an undirected graph denoted by G(R), whose vertex set is the set of all elements of R and distinct vertices x, y are joined by an edge in G(R) if and only if ... See full document
22
A graph associated to spectrum of a commutative ring
... Proof. By using the first isomorphism theorem for rings, R/Ker(f ) ∼ = R 0 . The result now immediately follows from Theorem 2.1 (i). Remark 2.3. Let R 0 be an extension ring of R and q ∈ Spec(R). A prime ideal Q ... See full document
13
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] ... See full document
8
Witt group of Hermitian forms over a noncommutative discrete valuation ring
... M ⊕ N ⊥ /N satisfies ∆ ⊥ = ∆. Thus (M ,h) ⊕ (N ⊥ /N , − h) is weakly metabolic. ¯ In the classical theory of regular symmetric bilinear forms over a commutative field F, orthogonal basis plays a key role in ... See full document
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