Browsing Department of Mathematics and Statistics by Author "3a720278-acad-4fc5-a178-88d24de85d95"
Now showing items 1-13 of 13
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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 ... -
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 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 ... -
On n-semiprimary ideals and n-pseudo valuation domains
(Taylor and Francis, 2020-08-14) -
On phi-Dedekind rings and phi-Krull rings
(University of Houston, 2005)The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R | R is a commutative ring with 1 and Nil(R) is a divided prime ... -
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 ... -
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 ... -
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 weakly 2-absorbing ideals of commutative rings
(University of Houston, 2013)Let R be a commutative ring with identity 1 not equal to 0. In this paper, we introduce the concept of a weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing ideal of R if whenever abc is not equal ... -
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 ... -
Some finiteness conditions on the set of overrings of a phi-ring
(University of Houston, 2008)Let H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is ... -
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.
