Results 1 to 10 of about 242 (16)

Functional identities on upper triangular matrix rings

Open Mathematics, 2020
Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), tll′$\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any ...
Yuan He, Chen Liangyun
doaj   +1 more source

On twists of modules over non-commutative Iwasawa algebras [PDF]

, 2015
It is well known that, for any finitely generated torsion module M over the Iwasawa algebra Z_p [[{\Gamma} ]], where {\Gamma} is isomorphic to Z_p, there exists a continuous p-adic character {\rho} of {\Gamma} such that, for every open subgroup U of ...
Jha, Somnath, Ochiai, Tadashi, Zábrádi, Gergely   +2 more
core   +3 more sources

Subrings which are closed with respect to taking the inverse

, 2007
Let S be a subring of the ring R. We investigate the question of whether S intersected by U(R) is equal to U(S) holds for the units. In many situations our answer is positive.
Szigeti, Jeno, van Wyk, Leon
core   +1 more source

Graphs from matrices - a survey

AKCE International Journal of Graphs and Combinatorics
Let R be a commutative ring with identity. For a positive integer [Formula: see text] let [Formula: see text] be the set of all n × n matrices over R and [Formula: see text] be the set of all non-zero matrices of [Formula: see text] The zero-divisor ...
T. Tamizh Chelvam
doaj   +1 more source

Extensions of Simple Modules and the Converse of Schur's Lemma

, 2009
The converse of Schur's lemma (or CSL) condition on a module category has been the subject of considerable study in recent years. In this note we extend that work by developing basic properties of module categories in which the CSL condition governs ...
Marks, Greg, Schmidmeier, Markus
core   +1 more source

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
doaj   +1 more source

Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three

, 2016
Given a positive integer d, the Kaplansky-Lvov conjecture states that the set of values of a multilinear noncommutative polynomial f on the matrix algebra M_d(C) is a vector subspace.
Dykema, Kenneth J., Klep, Igor
core   +1 more source

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 the Nilpotency in Matrix Algebras with Grassmann Entries [PDF]

, 2012
2010 Mathematics Subject Classification: 16R10, 15A75, 16S50.In 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
Rashkova, Tsetska
core  

Classification of certain types of maximal matrix subalgebras

, 2017
Let $M_n(K)$ denote the algebra of $n \times n$ matrices over a field $K$ of characteristic zero. A nonunital subalgebra $N \subset M_n(K)$ will be called a nonunital intersection if $N$ is the intersection of two unital subalgebras of $M_n(K ...
Eggers, John, Evans, Ron, Van Veen, Mark
core   +1 more source