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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 ...
On n-semiprimary ideals and n-pseudo valuation domains
(Taylor and Francis, 2020-08-14)
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 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 ...