Results 11 to 20 of about 931 (215)
Transitive reduction of a nilpotent boolean matrix [PDF]
Discrete Applied Mathematics, 1984 Given an acyclic digraph, a problem which frequently arises in applications consists in removing the maximum number of arcs without affecting reachability. This removal corresponds to a so-called transitive reduction of the adjacency matrix of the given digraph.
Hashimoto, Hiroshi
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Some nilpotent and locally nilpotent matrix groups [PDF]
Journal of Pure and Applied Algebra, 1989 The task of the paper under review is a detailed discussion of nilpotent and locally nilpotent matrix groups over ``special'' division rings. The notion of a ``special'' division ring is introduced by the author and denotes a division ring D with the following property: For every finite subset X of D and every finite subset Y of the subring R of D ...
Wehrfritz, B.A.F.
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On nilpotent subsemigroups of the matrix semigroup over an antiring [PDF]
Linear Algebra and its Applications, 2011 A semiring is an algebraic system \((R,+,\cdot)\) such that \((R,+)\) is a commutative semigroup with identity \(0\), \((R,\cdot)\) is a semigroup with identity \(1\), and ring-like distributivity holds. It is also assumed that \(0r=r0=0\) for all \(r\in R\) and that \(0\neq 1\).
Tan, Yi-Jia, Yi-Jia Tan
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Drużkowski matrix search and D-nilpotent automorphisms [PDF]
Indagationes Mathematicae, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
GORNI, Gianluca +2 more
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Finite Matrix Groups over Nilpotent Group Rings [PDF]
Journal of Algebra, 1996 Let \(\mathbb{Z} H\) be the integral group ring of a group \(H\). The authors study the group \(\text{SGL}_n(\mathbb{Z} H)\) of matrices of augmentation one over the group ring \(\mathbb{Z} H\), and relate the torsion of \(\text{SGL}_n(\mathbb{Z} H)\) to the torsion of \(H\).
Marciniak, Zbigniew S. +1 more
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The algebra generated by nilpotent elements in a matrix centralizer [PDF]
The Electronic Journal of Linear Algebra, 2021 For an arbitrary square matrix $S$, denote by $C(S)$ the centralizer of $S$, and by $C(S)_N$ the set of all nilpotent elements in $C(S)$. In this paper, we use the Weyr canonical form to study the subalgebra of $C(S)$ generated by $C(S)_N$. We determine conditions on $S$ such that $C(S)_N$ is a subalgebra of $C(S)$.
Ralph John De la Cruz, Eloise Misa
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Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size [PDF]
Linear Algebra and its ApplicationsIn this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix $B$ consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the nilpotent matrices that commute with $B$ by characterizing the corresponding partitions.
Bogdanić, Duško +4 more
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On Nilpotent Elements and Armendariz Modules [PDF]
MathematicsFor a left module MR over a non-commutative ring R, the notion for the class of nilpotent elements (nilR(M)) was first introduced and studied by Sevviiri and Groenewald in 2014 (Commun. Algebra, 42, 571–577).
Nazeer Ansari +4 more
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The Enumeration of Jordan′s Normal Form of k-nilpotent Matrices
Journal of Harbin University of Science and Technology, 2019 As a kind of special matrices, the nilpotent matrices has good properties. In this paper, we mainly discuss the enumeration problem of the Jordan′s normal form of 4-nilpotent matrix.
CHEN Jian-da, WANG Ping, ZHANG Lu
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A Matrix Model for Random Nilpotent Groups [PDF]
International Mathematics Research Notices, 2017 We study random torsion-free nilpotent groups generated by a pair of random words of length $\ell$ in the standard generating set of $U_n(\mathbb{Z})$. Specifically, we give asymptotic results about the step properties of the group when the lengths of the generating words are functions of $n$.
Delp, Kelly +2 more
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