Results 11 to 20 of about 62,458 (328)
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
openalex +3 more sources
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
openalex +4 more sources
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
openaire +2 more sources
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
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
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.
openaire +2 more sources
"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
doaj +1 more source
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
doaj +1 more source
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
openalex +3 more sources