Results 11 to 20 of about 1,197 (263)
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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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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"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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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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The étale cohomology ring of the ring of integers of a number field
Research in Number Theory, 2023 AbstractWe compute the cohomology ring $$H^*(X,{{\mathbb {Z}}}/n{{\mathbb {Z}}})$$ H ∗ ( X , Z /
Eric Ahlqvist, Magnus Carlson
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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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Cycles of polynomial mappings in two variables over rings of integers in quadratic fields
Central European Journal of Mathematics, 2004 Pezda T.
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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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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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