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Full Classification of Finite Singleton Local Rings
AxiomsThe main objective of this article is to classify all finite singleton local rings, which are associative rings characterized by a unique maximal ideal and a distinguished basis consisting of a single element.
Sami Alabiad, Yousef Alkhamees
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Local single ring theorem [PDF]
The Annals of Probability, 2017 33 pages, 2 figures. In version v2: hypothesis of the main theorem slightly weakened, proof adapted. In version v4: some of the proofs simplified, some of the appendix statements fixed, Remarks added, typos ...
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A Class of Local Non-Chain Rings of Order p5m
AxiomsThis study investigates finite commutative local non-chain rings characterized by the well-established invariants p, n, m, l, and k, where p denotes a prime number. We specifically focus on Frobenius local rings with length l=5 and an index of nilpotency
Alhanouf Ali Alhomaidhi +2 more
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Uniform definability of henselian valuation rings in the Macintyre language
, 2014 We discuss definability of henselian valuation rings in the Macintyre language $\mathcal{L}_{\rm Mac}$, the language of rings expanded by n-th power predicates. In particular, we show that henselian valuation rings with finite or Hilbertian residue field
Fehm, Arno, Prestel, Alexander
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On Linear Codes over Finite Singleton Local Rings
MathematicsThe study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings.
Sami Alabiad +2 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 This paper is dealed with a special local ring A and modules over A. Some properties of modules, that are constructed over the real plural algebra, are investigated. Moreover a module is constructed over the linear algebra of matrix Mmm(ℝ) and one of its
Erdoğan Fatma Özen +2 more
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Locally finite profinite rings
Journal of Algebra, 2014 17 ...
Jan Dobrowolski, Krzysztof Krupiński
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Frobenius Local Rings of Length 5 and Index of Nilpotency 3
MathematicsThis paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive characterization of Frobenius local rings of length l=5 and index of ...
Sami Alabiad, Alhanouf Ali Alhomaidhi
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The Metric Dimension and Local Metric Dimension of Relative Prime Graph
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2020 This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime.
Inna Kuswandari +2 more
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Local rings of bounded module type are almost maximal valuation rings
, 2005 It is shown that every commutative local ring of bounded module type is an almost maximal valuation ...
Couchot, Francois
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