Results 241 to 250 of about 386,457 (283)

A CHARACTERISATION OF MATRIX RINGS

Bulletin of the Australian Mathematical Society, 2022
AbstractWe prove that a ring R is an $n \times n$ matrix ring (that is, $R \cong \mathbb {M}_n(S)$ for some ring S) if and only if there exists a (von Neumann) regular element x in R such that $l_R(x) = R{x^{n-1}}$ . As applications, we prove some new results, strengthen some known results and provide easier proofs of other results.
DIMPLE RANI GOYAL, DINESH KHURANA
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Maximum Matrix Rings

Journal of the London Mathematical Society, 1943
Not ...
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Motions of Matrix Rings

Canadian Journal of Mathematics, 1964
Metric spaces in which the distances are not real numbers have been studied by several people (2, 3, 4, 7, 9). Any ringRtogether with a mapping,X—>ϕ(X), ofRinto a lattice A with 0 and 1 satisfyingis called a "lattice-valued ring," where the operations union, ∪, and intersection, ∩, are the usual lattice operations.
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Ring Closure Matrix

Current Organic Chemistry, 2015
We consider generalization of the terminal matrix of Zaretsky, in which only distances are listed between terminal vertices of acyclic graphs, to a condensed matrix for cyclic and polycyclic systems. Some 50 years ago Zaretsky has proved that the distance matrix between terminal vertices of acyclic graphs ...
Randić, Milan, Novič, Marjana, Plavšić, Dejan   +2 more
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Recognition of matrix rings II

Israel Journal of Mathematics, 1996
Let \(R\) be a ring with identity element 1. Various criteria are known for \(R\) to be a full \(n\) by \(n\) matrix ring, and the present paper follows on part I by \textit{J. C. Robson} [Commun. Algebra 19, No. 7, 2113-2124 (1991; Zbl 0731.16018)] who showed, for instance, that \(R\) is an \(n\) by \(n\) matrix ring if and only if \(R\) has elements \
Agnarsson, G., Amitsur, S. A., Robson, J. C.   +2 more
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Representation of tiled matrix rings as full matrix rings

Mathematical Proceedings of the Cambridge Philosophical Society, 1989
It can be very difficult to determine whether or not certain rings are really full matrix rings. For example, let p be an odd prime, let H be the ring of quaternions over the integers localized at p, and setThen T is not presented as a full matrix ring, but there is a subring W of H such that T ≅ M2(W). On the other hand, if we take H to be the ring of
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Learning Matrix Functions over Rings

Algorithmica, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bshouty, N. H., Tamon, C., Wilson, D. K.
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INVERTIBLE COMMUTATORS IN MATRIX RINGS

Journal of Algebra and Its Applications, 2011
In a matrix ring R = 𝕄2(S) where S is a commutative ring, we study equations of the form XY - YX = U ∈ GL 2(S), focusing on matrices in R that can appear as X or as XY in such equations. These are the completable and the reflectable matrices in R.
Khurana, Dinesh, Lam, T. Y.
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Formal Matrix Rings

2017
In this chapter, we define formal matrix rings of order 2 and formal matrix rings of arbitrary order n. Their main properties are considered and examples of such rings are given. We indicate the relationship between formal matrix rings, endomorphism rings of modules, and systems of orthogonal idempotents of rings.
Piotr Krylov, Askar Tuganbaev
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On Skew Triangular Matrix Rings

Algebra Colloquium, 2015
Let R be a ring with an endomorphism σ. We show that the clean property and various Armendariz-type properties of R are inherited by the skew matrix rings S(R,n,σ) and T(R,n,σ). They allow the construction of rings with a non-zero nilpotent ideal of arbitrary index of nilpotency which inherit various interesting properties of rings.
Habibi, M., Moussavi, A., Alhevaz, A.
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