Results 31 to 40 of about 88,527 (242)
ZERO DIVISORS AND TOPOLOGICAL DIVISORS OF ZERO IN CERTAIN BANACH ALGEBRAS
, 2023 In this paper we prove that an element $f\in \mathcal{A}(\mathbb{D})$ is a topological divisor of zero(TDZ) if and only if there exists $z_0 \in \mathbb{T}$ such that $f(z_0)=0.$ We also give a characterization of TDZ in the Banach algebra $L^\infty(\mu).$ Further, we prove that the multiplication operator $M_h$ is a TDZ in $\mathcal{B}(L^p(\mu))~(1 ...
Patel, Anurag Kumar, Chandra, Harish
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Distributive lattices and some related topologies in comparison with zero-divisor graphs [PDF]
Categories and General Algebraic Structures with Applications, 2021 In this paper,for a distributive lattice $\mathcal L$, we study and compare some lattice theoretic features of $\mathcal L$ and topological properties of the Stone spaces ${\rm Spec}(\mathcal L)$ and ${\rm Max}(\mathcal L)$ with the corresponding graph ...
Saeid Bagheri, mahtab Koohi Kerahroodi
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Valuation Rings with Zero Divisors [PDF]
Proceedings of the American Mathematical Society, 1971 Manis has developed a valuation theory for commutative rings which extends valuation theory for fields. However his results do not extend the characterization of valuation rings as domains of maximal partial homomorphisms. In this note we show that Manis’ theory also generalizes this aspect of valuation theory.
Kelly, P. H., Larsen, M. D.
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Upper dimension and bases of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2020 For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if .
S. Pirzada, M. Aijaz, S.P. Redmond
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On the eigenvalues of zero-divisor graph associated to finite commutative ring
AKCE International Journal of Graphs and Combinatorics, 2021 Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by is a simple graph whose vertex set is and two vertices are adjacent if and only if ...
S. Pirzada +2 more
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Rocky Mountain Journal of Mathematics, 2007 Let \(R\) be a commutative ring with unity. This paper studies \(Z(R)\) using homology group, where \(Z(R)\) is the set of zero-divisors in \(R\). In addition, the authors calculate the group \(H_{0}(R)\) in depth, in particular cases, and compute \(H_{1}(\frac{\mathbb{Z}}{p^{r}\mathbb{Z}})\) where \(p\) is a prime and \(r\geq 1\) is an integer.
Akhtar, Reza, Lee, Lucas
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On graphs with equal coprime index and clique number
AKCE International Journal of Graphs and Combinatorics, 2023 Recently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem.
Chetan Patil +2 more
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Graphs and Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hammack, Richard, Smith, Heather
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Rational Formulas for Traces in zero-dimensional Algebras [PDF]
, 2008 We present a rational expression for the trace of the multiplication map M_r in a finite-dimensional algebra of the form A:=K[x_1,...,x_n]/I in terms of the generalized Chow form of I.
D'Andrea, Carlos, Jeronimo, Gabriela
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Open Mathematics, 2015 Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor).
Nauman Syed Khalid, Shafee Basmah H.
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