Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Gargate, Ivan"'
Publikováno v:
Linear Algebra Appl., 674, 453-465, 2023
In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify that some multilinear polynomial is a central polynomial, or a trace z
Externí odkaz:
http://arxiv.org/abs/2210.05653
Publikováno v:
Isr. J. Math. 252, 337-354 (2022)
In this paper we prove that the image of multilinear polynomials evaluated on the algebra $UT_n(K)$ of $n\times n$ upper triangular matrices over an infinite field $K$ equals $J^r$, a power of its Jacobson ideal $J=J(UT_n(K))$. In particular, this sh
Externí odkaz:
http://arxiv.org/abs/2106.12726
Autor:
Gargate, Ivan, Gargate, Michael
Let $\mathbb{K}$ be a field such that $char(\mathbb{K})\nmid k$ and $char(\mathbb{K})\nmid k+1$. We describe all $(k+1)$-potent matrices over the group of upper triangular matrix. In the case that $\mathbb{K}$ is a finite field we show how to compute
Externí odkaz:
http://arxiv.org/abs/2009.04243
Autor:
Gargate, Ivan, Gargate, Michael
In the present article we shown a formula to compute the number of all matrices over the finite field $F$ whit prescribed eigenvalues. Using this formula we obtain one inequality for the number of $(k+1)$-potent elements over finite rings.
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Externí odkaz:
http://arxiv.org/abs/2008.13568
Autor:
Gargate, Ivan, Gargate, Michael
Let $R$ be an associative ring with identity $1$. We describe all matrices in $T_n(R)$ the ring of $n\times n$ upper triangular matrices over $R$ ($n\in \mathbb{N}$), and $T_{\infty}(R)$ the ring of infinite upper triangular matrices over $R$, satisf
Externí odkaz:
http://arxiv.org/abs/2008.11272
Autor:
Gargate, Ivan, Gargate, Michael
In this article we give various formulates for compute the number of all coninvolutions over the group of upper triangular matrix with entries into the ring of Gaussian integers module $p$ and the ring of Quaternions integers module $p$, with $p$ an
Externí odkaz:
http://arxiv.org/abs/2008.00575
Let $R$ be an associative ring with unity $1$ and consider that $2,k$ and $2k\in \mathbb{N}$ are invertible in $R$. For $m\geq 1$ denote by $UT_n(m,R)$ and $UT_{\infty}(m,R)$, the subgroups of $UT_n(R)$ and $UT_{\infty}(R)$ respectively, which have z
Externí odkaz:
http://arxiv.org/abs/2007.12305
Autor:
Gargate, Ivan, Gargate, Michael
We study sums of $k$-potent matrices. We show the conditions by which a complex matrix $A$ can be expressed as a sums of $k$-potent matrices. Also we obtain conditions by which a complex matrix $A$ can be expressed as a sum of finite order elements.
Externí odkaz:
http://arxiv.org/abs/2005.00601
Autor:
Gargate, Ivan, Gargate, Michael
Let $R$ be an associative ring with unity $1$ and consider $k\in \mathbb{N}$ such that $1+1+..+1=k$ is invertible. Denote by $\omega$ an arbitrary kth root of unity in $R$ and let $UT^{(k)}_{\infty}(R)$ be the group of upper triangular infinite matri
Externí odkaz:
http://arxiv.org/abs/2004.09012
Publikováno v:
In Linear Algebra and Its Applications 1 October 2023 674:453-465
