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Now showing items 1-10 of 13

#### 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 ...