Results 11 to 20 of about 1,202 (263)
Gauss Congruences in Algebraic Number Fields
Annales Mathematicae Silesianae, 2022 In this miniature note we generalize the classical Gauss congruences for integers to rings of integers in algebraic number fields.
Gładki Paweł, Pulikowski Mateusz
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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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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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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
Open Mathematics, 2004 Pezda T.
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