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On the dot product graph of a commutative ring II
(International Electronic Journal of Algebra, 2020)
In 2015, the second-named author introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × · · · × A (n times). We ...
Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory
(De Gruyter, 2020)
For a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph ...
The n-zero-divisor graph of a commutative semigroup
(Taylor and Francis, 2022-04-16)
Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zero-divisors of S, and n a positive integer. The zero-divisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct ...
On n-semiprimary ideals and n-pseudo valuation domains
(Taylor and Francis, 2020-08-14)
On Weakly 1-Absorbing Primary Ideals of Commutative Rings
(World Scientific, 2022)
Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is called a weakly 1-absorbing ...
On 1-absorbing primary ideals of commutative rings
(World Scientific, 2019-04-30)
Let R be a commutative ring with nonzero identity. In this paper, we introduce the concept of 1-absorbing primary ideals in commutative rings. A proper ideal I of R is called a 1-absorbing primary ideal of R if whenever ...
Graph of Linear Transformations Over R
(Springer, 2022-12-01)
In this paper, we study a connection between graph theory and linear transformations of finite dimensional vector spaces over R (the set of all real numbers). Let Rm, Rn be finite vector spaces over R, and let L be the set ...
Strong ring extensions andphi-pseudo-valuation rings
(University of Houston, 2006)
In this paper, we extend the concept of strong extensions of domains to the context of (commutative) rings with zero-divisors. We show that the theory of strong extensions of rings resembles that of strong extensions of domains.
On phi-Mori rings
(University of Houston, 2006)
A commutative ring R is said to be a phi-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map phi from the total quotient ring T(R) to R localized ...