Zobrazeno 1 - 10
of 150
pro vyhledávání: '"16k40"'
Autor:
Azarang, Alborz
The structure and the existence of maximal subrings in division rings are investigated. We see that if $R$ is a maximal subring of a division ring $D$ with center $F$ and $N(R)\neq U(R)\cup \{0\}$, where $N(R)$ is the normalizer of $R$ in $D$, then e
Externí odkaz:
http://arxiv.org/abs/2410.09051
Let $R$ be a ring and let $n\ge 2$. We discuss the question of whether every element in the matrix ring $M_n(R)$ is a product of (additive) commutators $[x,y]=xy-yx$, for $x,y\in M_n(R)$. An example showing that this does not always hold, even when $
Externí odkaz:
http://arxiv.org/abs/2404.18116
Autor:
Chipchakov, Ivan D.
This paper considers K\"{o}the's question of whether every associative locally finite-dimensional (abbr., LFD) central division algebra $R$ over a field $K$ is a normally locally finite (abbr., NLF) algebra over $K$, that is, whether every nonempty f
Externí odkaz:
http://arxiv.org/abs/2403.14564
Publikováno v:
J. Algebra 657 (2024) 363-378
Let $D$ be a noncommutative division ring. In a recent paper, Lee and Lin proved that if $\text{char}\, D\ne 2$, the only solution of additive maps $f, g$ on $D$ satisfying the identity $f(x) = x^n g(x^{-1})$ on $D\setminus \{0\}$ with $n\ne 2$ a pos
Externí odkaz:
http://arxiv.org/abs/2403.13650
In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with respect to
Externí odkaz:
http://arxiv.org/abs/2403.08595
Autor:
Lee, Tsiu-Kwen, Lin, Jheng-Huei
Publikováno v:
J. Algebra 647 (2024) 492-514
We study the functional identity $G(x)f(x)=H(x)$ on a division ring $D$, where $f \colon D\to D$ is an additive map and $G(X)\ne 0, H(X)$ are generalized polynomials in the variable $X$ with coefficients in $D$. Precisely, it is proved that either $D
Externí odkaz:
http://arxiv.org/abs/2401.03112
Surface groups are known to be the Poincar\'e Duality groups of dimension two since the work of Eckmann, Linnell and M\"uller. We prove a prosolvable analogue of this result that allows us to show that surface groups are profinitely (and prosolvably)
Externí odkaz:
http://arxiv.org/abs/2312.12293
In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major cases, addi
Externí odkaz:
http://arxiv.org/abs/2311.06966
Autor:
Podlogar, Gregor
We study so called weakly-periodic twisted-multiplicative automorphisms of the free skew-field. In particular, we show that any automorphism of a free skew-field that is defined by a periodic automorphism of a free group is equivalent to a diagonal a
Externí odkaz:
http://arxiv.org/abs/2304.07818
Let $F$ be a field with at least three elements and $G$ a locally finite group. This paper aims to show that if either $F$ is algebraically closed or the characteristic of $F$ is positive, then an element in the group algebra $FG$ is a product of uni
Externí odkaz:
http://arxiv.org/abs/2211.09468