Results 21 to 30 of about 53 (53)

Amitsur's theorem, semicentral idempotents, and additively idempotent semirings

Open Mathematics
The article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation.
Rachev Martin, Trendafilov Ivan
doaj   +1 more source

On nilpotent matrices that are unit-regular

In this paper, we characterize regular nilpotent 2 × 2 matrices over Bézout domains and prove that they are unit-regular. We also demonstrate that nilpotent n × n matrices over division rings are unit-regular.
CĂLUGĂREANU, Grigore
core   +1 more source

Fejér–Riesz factorization in the QRC-subalgebra and circularity of the quaternionic numerical range

Journal Article, Faculty of Natural and Agricultural Sciences, Pure and Applied Analytics -- Potchefstroom CampusWe provide a characterization when the quaternionic numerical range of a matrix is a closed ball with center 0.
Van Straaten, Madelein, Vander Merwe, Alma, Woerdeman, Hugo J   +2 more
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Idempotents which are products of two nilpotents

Special Matrices
Over any GCD (greatest common divisor) commutative domain we show that the nontrivial 2×22\times 2 idempotent matrices are products of two nilpotent matrices. In order to find explicitly such decompositions, two procedures are described.
Călugăreanu Grigore, Pop Horia F.
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The c-numerical range of a quaternion skew-Hermitian matrix is convex

Journal Article, Faculty of Natural and Agricultural Sciences, Pure and Applied Analytics-- Potchefstroom CampusWe show that the c-numerical range of a non-scalar skew-Hermitian quaternion matrix is convex.
Thiersen, Madelein, Vander Merwe, Alma, Woerdeman, Hugo J   +2 more
core   +1 more source

Subspace profiles over finite fields and q-Whittaker expansions of symmetric functions

Forum of Mathematics, Sigma
Bender, Coley, Robbins, and Rumsey posed the problem of counting the number of subspaces which have a given profile with respect to a linear endomorphism defined on a finite vector space.
Samrith Ram
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Jordan left derivations in infinite matrix rings

Demonstratio Mathematica
Let RR be a unital associative ring. Our motivation is to prove that left derivations in column finite matrix rings over RR are equal to zero and demonstrate that a left derivation d:T→Td:{\mathcal{T}}\to {\mathcal{T}} in the infinite upper triangular ...
Zhang Daochang, Ma Leiming, Hu Jianping, Sun Chaochao   +3 more
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The perturbation of Drazin inverse and dual Drazin inverse

Special Matrices
In this study, we derive the Drazin inverse (A+εB)D{\left(A+\varepsilon B)}^{D} of the complex matrix A+εBA+\varepsilon B with Ind(A+εB)>1{\rm{Ind}}\left(A+\varepsilon B)\gt 1 and Ind(A)=k{\rm{Ind}}\left(A)=k and the group inverse (A+εB)#{\left(A ...
Wang Hongxing, Cui Chong, Wei Yimin
doaj   +1 more source

Determinants of tridiagonal matrices over some commutative finite chain rings

Special Matrices
Diagonal matrices and their generalization in terms of tridiagonal matrices have been of interest due to their nice algebraic properties and wide applications.
Jitman Somphong, Sricharoen Yosita
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1-Sylvester matrices

Special Matrices
A nonzero element aa is called 1-Sylvester in a ring RR, if there exist b,c∈Rb,c\in R such that 1=ab+ca1=ab+ca. In this article, we study such elements, mainly in matrix rings over commutative rings.
Călugăreanu Grigore
doaj   +1 more source