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Search: MSC category 16W20 ( Automorphisms and endomorphisms )

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1. CMB 2012 (vol 56 pp. 584)

Liau, Pao-Kuei; Liu, Cheng-Kai
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)

Jin, Hai Lan; Doh, Jaekyung; Park, Jae Keol
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)

Chebotar, M. A.; Ke, W.-F.; Lee, P.-H.; Shiao, L.-S.
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)

Brešar, Matej; Martindale, W. S.; Miers, C. Robert
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

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