KAROUBI’S RELATIVE CHERN CHARACTER, THE RIGID SYNTOMIC REGULATOR, AND THE BLOCH–KATO EXPONENTIAL MAP [PDF]
Forum of Mathematics, Sigma, 2014 We construct a variant of Karoubi’s relative Chern character for smooth separated schemes over the ring of integers in a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le
GEORG TAMME
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Factorization of rings of integer-valued rational functions [PDF]
Communications in Algebra, 2023 $\DeclareMathOperator{\Int}{Int}\DeclareMathOperator{\IntR}{Int{}^\text{R}}$For a domain $D$, the ring $\Int(D)$ of integer-valued polynomials over $D$ is atomic if $D$ satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain $V$, the ring $\IntR(V)$ of integer-valued rational functions over $V$ is ...
Baian Liu
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On Algebraic Properties of Primitive Eisenstein Integers with Applications in Coding Theory [PDF]
EntropyAn even Eisenstein integer is a multiple of an Eisenstein prime of the least norm. Otherwise, an Eisenstein integer is called odd. An Eisenstein integer that is not an integer multiple of another one is said to be primitive.
Abdul Hadi +3 more
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Certifying rings of integers in number fields [PDF]
Proceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs14 pages.
Anne Baanen +2 more
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Codes Over Rings of Algebraic Integers
Journal of Communication and Information Systems, 1998 1 modulo 6 if d = -3.These alphabets are isomorphic to the field GF(p), and both will be denoted by A. Associated to any two elements of G F (p) , there is a distance, which is called Mannheim distance between the corresponding elements in A. Four classes of codes are proposed.One class is designed to correct one Mannbeim error, another to correct ...
Osvaldo Milaré Favareto +3 more
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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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Partial Foundation of Neutrosophic Number Theory [PDF]
Neutrosophic Sets and Systems, 2021 The aim of this paper is to establish a partial foundation of number theoretical concepts in the neutrosophic ring of integers 𝑍(𝐼) because it is based on a partial order relationship.
Mohammad Abobala
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On Phi-Euler's Function in Refined Neutrosophic Number Theory and The Solutions of Fermat's Diophantine Equation [PDF]
Neutrosophic Sets and Systems, 2023 The objective of this paper is to answer the open problem proposed about the validity of phi-Euler’s theorem in the refined neutrosophic ring of integers 𝑍(𝐼1,𝐼2) .
Josef Al Jumayel +2 more
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Neutrosophic Linear Diophantine Equations with Two Variables [PDF]
Neutrosophic Sets and Systems, 2020 This paper studies for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers.
Hasan Sankari, Mohammad Abobala
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An Introduction to Refined Neutrosophic Number Theory [PDF]
Neutrosophic Sets and Systems, 2021 Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell's equation
Mohammad Abobala, Muritala Ibrahim
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