Results 11 to 20 of about 1,179 (268)
On The Symbolic 2-Plithogenic Number Theory and Integers [PDF]
Neutrosophic Sets and Systems, 2023 The objective of this paper is to study for the first time the foundational concepts of number theory in 2-plithogenic rings of integers, where concepts such as symbolic 2-plithogenic congruencies, division, semi primes, and greatest common divisors.
Hamiyet Merkepci, Ammar Rawashdeh
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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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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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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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"Exotic" binary number systems for rings of Gauss and Eisenstein integers [PDF]
Компьютерная оптика, 2018 The paper considers nonstandard binary number systems for rings of Gauss and Eisenstein integers. The principal difference ("exoticism") of such number systems from the canonical number systems introduced by I.
Vladimir Chernov
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Determinants of some special matrices over commutative finite chain rings
Special Matrices, 2020 Circulant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal matrices over
Jitman Somphong
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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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Approximatting rings of integers in number fields [PDF]
Journal de théorie des nombres de Bordeaux, 1994 In this paper we study the algorithmic problem of finding the ring of integers of a given algebraic number field. In practice, this problem is often considered to be well-solved, but theoretical results indicate that it is intractable for number fields that are defined by equations with very large coefficients.
Lenstra, H.W., Buchmann, J.A.
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Algebraic Structure of Neutrosophic Duplets in Neutrosophic Rings
Neutrosophic Sets and Systems, 2018 The concept of neutrosophy and indeterminacy I was introduced by Smarandache, to deal with neutralies. Since then the notions of neutrosophic rings, neutrosophic semigroups and other algebraic structures have been developed.
Vasantha W.B +2 more
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