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    On the dot product graph of a commutative ring II 

    Abdulla, Mohammad Ahmad; Badawi, Ayman (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 ...
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    Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory 

    Badawi, Ayman; Rissner, Roswitha (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 ...
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    The n-zero-divisor graph of a commutative semigroup 

    Anderson, David F.; Badawi, Ayman (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 ...
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    On n-semiprimary ideals and n-pseudo valuation domains 

    Anderson, David F.; Badawi, Ayman (Taylor and Francis, 2020-08-14)
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    n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey 

    Badawi, Ayman (Springer, 2017)
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    On Weakly 1-Absorbing Primary Ideals of Commutative Rings 

    Badawi, Ayman; Celikel, Ece Yetkin (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 ...
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    On 1-absorbing primary ideals of commutative rings 

    Badawi, Ayman; Celikel, Ece Yetkin (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 

    Badawi, Ayman; El-Ashi, Yasmine Ahmed (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 ...
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    Strong ring extensions andphi-pseudo-valuation rings 

    Badawi, Ayman; Dobbs, David E. (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.
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    On phi-Mori rings 

    Badawi, Ayman; Lucas, Thomas G. (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 ...
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    Badawi, Ayman (13)
    Anderson, David F. (3)Celikel, Ece Yetkin (2)Abdulla, Mohammad Ahmad (1)Darani, Ahmad Yousefian (1)Dobbs, David E. (1)El-Ashi, Yasmine Ahmed (1)Jaballah, Ali (1)Lucas, Thomas G. (1)Rissner, Roswitha (1)Subject2-absorbing ideal (3)Annihilator graph (3)Zero-divisor graph (3)1-absorbing primary ideal (2)2-absorbing primary ideal (2)Dot product graph (2)n-absorbing ideal (2)Primary ideal (2)Prime ideal (2)Total graph (2)... View MoreDate Issued2020 - 2022 (6)2010 - 2019 (3)2005 - 2009 (4)Has File(s)Yes (13)

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