Results 21 to 30 of about 62,458 (328)

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
doaj   +1 more source

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, Taras Vasylyshyn, Andriy Zagorodnyuk   +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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Some Additive Combinatorics Problems in Matrix Rings [PDF]

, 2010
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the ...
A.N. Skorobogatov, Alina Ostafe, Corneliu Hoffman, D. Covert, D. Hart, E. Kowalski, E.S. Croot, Florian Luca, G. Laumon, H. Iwaniec, H.A. Helfgott, I.E. Shparlinski, Igor E. Shparlinski, J. Bourgain, L.E. Dickson, M.-C. Chang, M.-C. Chang, N. Katz, P.X. Gallagher, Ron Ferguson, T. Tao, W. Bruns, W. Luo, É. Fouvry, É. Fouvry   +24 more
core   +3 more sources

Algebraic Structure of Neutrosophic Duplets in Neutrosophic Rings , Q∪I, and [PDF]

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, Ilanthenral Kandasamy, Florentin Smarandache   +2 more
doaj   +1 more source

Polynomial multiple recurrence over rings of integers [PDF]

Ergodic Theory and Dynamical Systems, 2015
We generalize the polynomial Szemerédi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root modulo every ideal. This leads to the existence of new polynomial configurations in positive-density subsets of $\mathbb{Z}^{m}$ and strengthens and extends recent results ...
Robertson, Donald, Bergelson, Vitaly
openaire   +3 more sources

Finding Minimal Units In Several Two-Fold Fuzzy Finite Neutrosophic Rings [PDF]

Neutrosophic Sets and Systems
In this paper, we have defined the concept of minimal units in finite two-fold fuzzy neutrosophic rings modulo integers as a generalization of classical elements of the group of units of the mentioned neutrosophic rings.
Raed Hatamleh, Ayman Hazaymeh
doaj   +1 more source

Bounds for Coding Theory over Rings

Entropy, 2022
Coding theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. It has been well established that, with the generalization of the algebraic structure to rings, there is
Niklas Gassner, Marcus Greferath, Joachim Rosenthal, Violetta Weger   +3 more
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On some integral representations of groups and global irreducibility. [PDF]

International Journal of Group Theory, 2018
Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings.
Dmitry Malinin
doaj   +1 more source