A note on $σ$-reversibility and $σ$-symmetry of skew power series rings

Details A note on $σ$-reversibility and $σ$-symmetry of skew power series rings A note on $σ$-reversibility and $σ$-symmetry of skew power series rings

2009-02-23

arxiv.org/abs/0902.3992v1

International Journal of Algebra, Vol. 3, 2009, no. 9, 435 - 442

Mathematics

Rings and Algebras

8

Scientific paper

Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we study the transfert of the symmetry ($\sigma$-symmetry) and reversibility ($\sigma$-reversibility) from $R$ to its skew power series ring $R[[x;\sigma]]$. Moreover, we study on the relationship between the Baerness, quasi-Baerness and p.p.-property of a ring $R$ and these of the skew power series ring $R[[x;\sigma]]$ in case $R$ is right $\sigma$-reversible. As a consequence we obtain a generalization of \cite{hong/2000}.

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