Expand all Collapse all | Results 1 - 4 of 4 |
1. CMB 2012 (vol 56 pp. 584)
On Automorphisms and Commutativity in Semiprime Rings Let $R$ be a semiprime ring with center
$Z(R)$. For $x,y\in R$, we denote by $[x,y]=xy-yx$ the commutator of
$x$ and $y$. If $\sigma$ is a non-identity automorphism of $R$ such
that
$$
\Big[\big[\dots\big[[\sigma(x^{n_0}),x^{n_1}],x^{n_2}\big],\dots\big],x^{n_k}\Big]=0
$$
for all $x \in R$, where $n_{0},n_{1},n_{2},\dots,n_{k}$ are fixed
positive integers, then there exists a map $\mu\colon R\rightarrow Z(R)$
such that $\sigma(x)=x+\mu(x)$ for all $x\in R$. In particular, when
$R$ is a prime ring, $R$ is commutative.
Keywords:automorphism, generalized polynomial identity (GPI) Categories:16N60, 16W20, 16R50 |
2. CMB 2009 (vol 52 pp. 564)
Group Actions on Quasi-Baer Rings A ring $R$ is called {\it quasi-Baer} if the right
annihilator of every right ideal of $R$ is generated by an
idempotent as a right ideal. We investigate the quasi-Baer
property of skew group rings and fixed rings under a finite group
action on a semiprime ring and their applications to
$C^*$-algebras.
Various examples to illustrate and
delimit our results are provided.
Keywords:(quasi-) Baer ring, fixed ring, skew group ring, $C^*$-algebra, local multiplier algebra Categories:16S35, 16W22, 16S90, 16W20, 16U70 |
3. CMB 2005 (vol 48 pp. 355)
On Maps Preserving Products Maps preserving certain algebraic properties of elements
are often studied in Functional Analysis and Linear Algebra. The
goal of this paper is to discuss the relationships among these
problems from the ring-theoretic point of view.
Categories:16W20, 16N50, 16N60 |
4. CMB 1998 (vol 41 pp. 452)
Dependent automorphisms in prime rings For each $n\geq 4$ we construct a class of examples of a minimal
$C$-dependent set of $n$ automorphisms of a prime ring $R$, where $C$
is the extended centroid of $R$. For $n=4$ and $n=5$ it is shown that
the preceding examples are completely general, whereas for $n=6$ an
example is given which fails to enjoy any of the nice properties of
the above example.
Categories:16N60, 16W20 |