Results 11 to 20 of about 2,443 (266)

∗-Regularity in the ring of matrices over the ring of integers modulo 𝑛 [PDF]

Songklanakarin Journal of Science and Technology (SJST), 2023
For any positive integer 𝑛 ≥ 2, we give necessary and sufficient conditions of the existence of the Moore-Penrose inverse of any square matrix over the ring of integers modulo 𝑛.
Wannisa Apairat, Sompong Chuysurichay
doaj  

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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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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On Generation of the Groups $SL_n(\mathbb{Z}+i\mathbb{Z})$ and $PSL_n(\mathbb{Z}+i\mathbb{Z})$ by Three Involutions, Two of Which Commute

Известия Иркутского государственного университета: Серия "Математика", 2022
M. C. Tamburini and P. Zucca proved that the special linear group of dimension greater than 13 over the ring of Gaussian integers is generated by three involutions, two of which commute (J. of Algebra, 1997).
R. I. Gvozdev, Ya.N. Nuzhin, T. B. Shaipova   +2 more
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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
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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
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Trivial units for group rings over rings of algebraic integers [PDF]

Proceedings of the American Mathematical Society, 2005
Let G G be a nontrivial torsion group and R R be the ring of integers of an algebraic number field. The necessary and sufficient conditions are given under which R G RG has only trivial units.
Herman, Allen, Li, Yuanlin
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Endomorphisms and Product Bases of the Baer-Specker Group

International Journal of Mathematics and Mathematical Sciences, 2009
The endomorphism ring of the group of all sequences of integers, the Baer-Specker group, is isomorphic to the ring of row finite infinite matrices over the integers.
E. F. Cornelius
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