Results 21 to 30 of about 131,023 (367)
On graphs associated to ring of Guassian integers and ring of integers modulo n
Acta Universitatis Sapientiae, Informatica, 2022 Abstract For a commutative ring R with identity 1, the zero-divisor graph of R, denoted by Ξ(R), is a simple graph whose vertex set is the set of non-zero zero divisors Z*(R) and the two vertices x and y β Z*(R) are adjacent if and only if xy = 0.
Pirzada S., Bhat M. Imran
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Elimination theory for the ring of algebraic integers.
Journal fΓΌr die reine und angewandte Mathematik (Crelles Journal), 1988 Let \(\mathcal R\) be the ring of all algebraic integers, \(\mathcal R\subset\mathbb C\). The author proves the following elimination theorem: Each elementary problem about \(\mathcal R\) can be effectively reduced to a finite number of ideal membership questions about the algebraic integers constructed by a simple algorithm from the parameters of the ...
L. Dries
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SOME PROPERTIES OF THE ZERO-DIVISOR GRAPH FOR THE RING OF GAUSSIAN INTEGERS MODULO n [PDF]
Glasgow Mathematical Journal, 2011 Emad Abu Osba +2 more
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β-Regularity in the ring of matrices over the ring of integers modulo π [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 For any positive integer π β₯ 2, we give necessary and sufficient conditions of the existence of the Moore-Penrose inverse of any square matrix over the ring of integers modulo π.
Wannisa Apairat, Sompong Chuysurichay
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Statistics of K-groups modulo p for the ring of integers of a varying quadratic number field [PDF]
Tunisian Journal of Mathematics, 2017 For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgroup of
Bruce W. Jordan +4 more
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A novel approach to find partitions of $ Z_{m} $ with equal sum subsets via complete graphs
AIMS Mathematics, 2021 In mathematics and computer sciences, the partitioning of a set into two or more disjoint subsets of equal sums is a well-known NP-complete problem, also referred to as partition problem.
M. Haris Mateen, Muhammad Khalid Mahmmod
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Polyadic rings of p-adic integers
Symmetry, 2022 In this note we, first, recall that the sets of all representatives of some special ordinary residue classes become $\left( m,n\right) $-rings. Second, we introduce a possible $p$-adic analog of the residue class modulo a $p$-adic integer. Then, we find the relations which determine, when the representatives form a $\left( m,n\right) $-ring.
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A LeVeque-type inequality on the ring of p-adic integers [PDF]
International Journal of Number Theory, 2019 We derive an inequality on the discrepancy of sequences on the ring of [Formula: see text]-adic integers [Formula: see text] using techniques from Fourier analysis.
N. Somasunderam
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Clean group rings over localizations of rings of integers [PDF]
Journal of Pure and Applied Algebra, 2020 A ring $R$ is said to be clean if each element of $R$ can be written as the sum of a unit and an idempotent. In a recent article (J. Algebra, 405 (2014), 168-178), Immormino and McGoven characterized when the group ring $\mathbb Z_{(p)}[C_n]$ is clean, where $\mathbb Z_{(p)}$ is the localization of the integers at the prime $p$.
Li, Yuanlin, Zhong, Qinghai
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Rings of Multisets and Integer Multinumbers [PDF]
Mathematics, 2022 In the paper, we consider a ring structure on the Cartesian product of two sets of integer multisets. In this way, we introduce a ring of integer multinumbers as a quotient of the Cartesian product with respect to a natural equivalence. We examine the properties of this ring and construct some isomorphisms to subrings of polynomials and Dirichlet ...
Yuriy Chopyuk +2 more
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