Results 1 to 10 of about 615 (122)
A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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IEEE Access, 2023 A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
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General Kloosterman sums over the ring of Gaussian integers [PDF]
Ukrainian Mathematical Journal, 2007 The general Kloosterman sum K(m, n; k; q) over ℤ was studied by S. Kanemitsu, Y. Tanigawa, Yuan Yi, and Wenpeng Zhang in their research of the problem of D. H. Lehmer. In the present paper, we obtain similar estimates for K(α, β; k; γ) over ℤ[i]. We also consider the sum \(\tilde K(\alpha ,\beta ;h,q;k)\), which does not have an analog in the ring ℤ ...
exaly +2 more sources
On the Line Graph of the Complement Graph for the Ring of Gaussian Integers Modulo n
Open Journal of Discrete Mathematics, 2012 The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given.
Manal Ghanem, Khalida Nazzal
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The group of primitive Pythagorean triples over Gaussian integers [PDF]
Heliyon, 2023 Ekkasit Sangwisut
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Известия Иркутского государственного университета: Серия "Математика", 2022 M. C. Tamburini and P. Zucca proved that the special linear group of dimension greater than 13 over the ring of Gaussian integers is generated by three involutions, two of which commute (J. of Algebra, 1997).
R. I. Gvozdev +2 more
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Enumeration of Involutions of Finite Rings
Journal of New Theory, 2021 In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution of a ring R is an element with the property that x^2-1=0 for some x in R.
Sajana Shaık, Chalapathi Tekurı
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International Journal of Mathematics and Mathematical Sciences, 2021 For a Gaussian prime π and a nonzero Gaussian integer β=a+bi∈ℤi with a≥1 and β≥2+2, it was proved that if π=αnβn+αn−1βn−1+⋯+α1β+α0≕fβ where n≥1, αn∈ℤi\0, α0,…,αn−1 belong to a complete residue system modulo β, and the digits αn−1 and αn satisfy certain ...
Phitthayathon Phetnun +2 more
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Solvability of certain exponential Lebesgue-Nagell equations 𝑥 2 + 𝑝 𝑚 = 𝑦 [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 In this article, we first investigate the exponential Lebesgue-Nagell equation as shown in the title. Eventually, we can establish a necessary and sufficient criterion for having an integer solution to such an equation under the conditions that 𝑝 ≡ 3 ...
Patcharee Wongsason, Sawian Jaidee
doaj
The cubic mapping graph for the ring of Gaussian integers modulo n [PDF]
Czechoslovak Mathematical Journal, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wei, Yangjiang, Nan, Jizhu, Tang, Gaohua
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