Finite commutative ring
Some properties of the nilradical and non-nilradical graphs over finite commutative ring \(\mathbb{Z}_n\)
... The concept of zero-divisor graph was introduced by I. beck in 1988 but the most common definition of zero-divisor graph given by D. F. Anderson and P. S. Livingston in 1999 is as follows: “Let R be a commutative ...
10
On the Structure of Commutative Rings with ${\bf {p_1}^{k_1}\cdots {p_n}^{k_n} Zero-Divisors
... a finite commutative ring R is local if and only if |Z(R)| = p k and |R| = p n for some prime number p and n > k ≥ 0 (Theorem ...characterize commutative rings R with |Z(R)| = p k where 1 ≤ ...
14
ℤ4 codes and their Gray map images as orthogonal arrays
... We show that a linear code over any finite commutative ring with identity has strength one less than the minimum weight of its dual Theorem 3.1.. The two questions are related.[r] ...
7
Self Additive Inverse Elements of Neutrosophic Rings and Fields
... a finite commutative ring with ...a finite commutative ring with unity 1 of integers 0, 1, ...a finite field of order n if and only if n is a ...
10
Generalization of Schur's Lemma in Ring Representations on Modules over a Commutative Ring
... the ring R is Artinian by using categorical approach [3],[4], and used the result to study the repre- sentation of finite dimension of algebra ...of finite F -algebras on vector spaces over a field F ...
11
THE NON-COMMUTATIVE FULL RHOTRIX RING AND ITS SUBRINGS
... rhotrix ring had been introduced. The subrings of the non-commutative full rhotrix ring were ...rhotrix ring is embedded on the well-known non-commutative full matrix ...rhotrix ...
13
A combinatorial commutativity property for rings
... 2. Preliminaries. We begin with some notation. Let R be an arbitrary ring, not nec- essarily with 1. The symbols D , N , Z , and C(R) denote the set of zero divisors, the set of nilpotent elements, the center, and ...
6
On Commutativity of Rings Under Certain Polynomial Constraints
... a contradiction. Using similar arguments as used above, It can be easily shown that there does not exists any ring among the remaining four rings as discussed above which is satisfying the property ( P 2 ) and in ...
7
On Quasi-weak Commutative Boolean-like Near-Rings
... weak commutative Boolean-like ...quasi-weak commutative near-ring in ...near ring (right) and prove that every quasi-weak ...near ring can be imbedded into a quasi weak ...
9
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
The k Zero Divisor Hypergraph of a Commutative Ring
... [6] D. F. Anderson, A. Frazier, A. Lauve, and P. S. Livingston, “The zero-divisor graph of a com- mutative ring. II,” in Ideal Theoretic Methods in Commutative Algebra (Columbia, MO, 1999), vol. 220 of ...
15
Analysis of Algebra of Complex Analysis
... The review analysis the complex analysis in algebraic geometry one reviews complex analytic and algebraic varieties, maps between such spaces (the easiest case being holomorphic and algebraic capacities) and analytic and ...
15
A variant of the primitive element theorem for separable extensions of a commutative ring
... Given a ring extension 𝑆 ⊇ 𝑅 we say that 𝑆 has a primitive element over 𝑅 if there exists 𝛼 ∈ 𝑆 such that 𝑆 = 𝑅[𝛼]. As it is well known, any finite separable field extension has a primitive element. Although this ...
8
On the lattice of cyclic codes over finite chain rings
... A b s t r ac t . In this paper, R is a finite chain ring of invariants (q, s), and ℓ is a positive integer fulfilling gcd(ℓ, q) = 1. In the language of q-cyclotomic cosets modulo ℓ, the cyclic codes over R ...
17
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
A commutative Bezout \(PM^{\ast}\) domain is an elementary divisor ring
... which is not adequate but which does have the property that each nonzero prime ideal is contained in a unique maximal ideal. In this paper we show that a commutative Bezout domain in which each nonzero prime ideal ...
7
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
Classical 2-absorbing Submodules of Modules Over Commutative Rings
... In this paper we introduce the definition of classical 2-absorbing submodules. A proper sub- module N of an R-module M is called classical 2-absorbing submodule if whenever a, b, c ∈ R and m ∈ M with a bcm ∈ N, then a bm ...
14
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
Transparency of Polynomial Ring Over a Commutative Noetherian Ring
... local ring, σ an automorphism of R and δ a σ-derivation of ...local ring R with a nilpotent maximal ideal, the ore extension R[ x ; σ, δ] will or will not be 2-primal depending on the δ-stability of the ...
7