Results 1 to 10 of about 165,979,158 (232)
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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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 Γ(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 ∈ Z*(R) are adjacent if and only if xy = 0.
Pirzada S., Bhat M. Imran
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Implicit linear difference equations over a non-Archi-medean ring
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2021 Over any field an implicit linear difference equation one can reduce to the usual explicit one, which has infinitely many solutions ~ one for each initial value.
Anna Goncharuk
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On (m, k) -type elements in the ring of integers modulo n [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 An element a in a ring R is said to be of (m, k)-type if a m = a k where m and k are positive integers with m > k ≥ 1. Let Xn(m, k) be the set of all (m, k)-type elements, X * n(m, k) be the set of all nonzero (m, k)-type elements, and Sn(m, k) be ...
Phoschanun Ratanaburee +2 more
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Computing in quotients of rings of integers [PDF]
LMS Journal of Computation and Mathematics, 2014 AbstractWe develop algorithms to turn quotients of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and their behavior under certain quotients.
Claus Fieker, Tommy Hofmann
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Euclidean Rings of Algebraic Integers [PDF]
Canadian Journal of Mathematics, 2004 AbstractLet K be a finite Galois extension of the field of rational numbers with unit rank greater than 3. We prove that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann hypothesis for Dedekind zeta functions.
Harper, Malcolm, Murty, M. Ram
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∗-Regularity in the ring of matrices over the ring of integers modulo 𝑛 [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 For any positive integer 𝑛 ≥ 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 𝑛.
Wannisa Apairat, Sompong Chuysurichay
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