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Matrix representability of nilpotent products of groups
Mathematical Notes of the Academy of Sciences of the USSR, 1973Necessary and sufficient conditions are determined for the matrix representability over a field of zero characteristic of the second nilpotent product of arbitrary matrix groups and of an arbitrary nilpotent product of Abelian matrix groups.
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On fine matrix representations of nilpotent operators
Acta Mathematica Sinica, 1985Let H be a complex Hilbert space and A be a nilpotent operator of order n. Put \(H_ k=\ker A^{k+1}\Theta \ker A^ k\), \(P_ k=P_{H_ k}\), \(A_ k=P_ kAP_{k+1}\).
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On the Nilpotence of the S-Radical in Matrix Near-Rings
2005Let R be a zero-symmetric near-ring with identity and \(M\)n(R) the matrix near-ring associated with R. We prove that the s-radicals Js(R) and Js(\(M\)n(R)) satisfy (Js(R))+ ⊆ Js (Mn(R)), where \(M\)n(R) satisfies the DCCL. We also show that A+ ⊆ A, where A and A are the s-socles of R and \(M\)n(R), respectively.
John F.T. Hartney, Anthony M. Matlala
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Real Neutrosophic Matrix and Real Nilpotent Neutrosophic Matrix
Annals of Pure and Applied MathematicsReal neutrosophic nilpotent matrices are a special class of matrices characterized by their neutrosophic components, which quantify the indeterminacy in their elements. This paper explores the properties and important results related to real neutrosophic nilpotent matrices.
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The Idempotent and Nilpotent Elements of a Matrix
American Journal of Mathematics, 1936openaire +2 more sources
On the Nilpotency in Matrix Algebras with Grassmann Entries
2017In the paper we consider some classes of subalgebras of Mn(E) (for a given n and any n) for E being the Grassmann algebra. We give an estimation of the index of nilpotency of the commutators of length 2 for these classes of matrix algebras.
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THE CLASSICAL CANONICAL FORM OF A NILPOTENT MATRIX
The Quarterly Journal of Mathematics, 1955openaire +2 more sources

