$$

\inf \left \{ \frac{\zeta (rs)}{\zeta(r)}, \frac{\zeta (sr)}{\zeta (r)}

\bigm | 0\ne r\in R \right \} >0.

$$

The given example shows that the demand that $s^k R\subseteq Rs$ for some natural number $k$ can't be substituted for demand that in ring $R$ the right condition Ore is fulfilled concerning multiplicative system $S=\{s^i|i=1,2,\dots \}$.

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