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Now showing items 1-10 of 13

#### 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 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 ...

#### 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 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 ...

#### 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 ...

#### 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 ...

#### 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)