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Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we studythe 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 powerseries ring $R[[x;\sigma]]$ in case $R$ is right $\sigma$-reversible. As aconsequence we obtain a generalization of \cite{hong/2000}.

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