  We study a nonlinear spin dynamics of a ferromagnetic ring in a vortex state
induced by the spin-polarized current. We also suggest to use the ferromagnetic
ring as a free layer of a coreless vortex spin-transfer nano-oscillator. The
calculated working frequency is about several GHz, that is much higher than the
gyromode frequency of the disk-based vortex oscillator. The response of the
vortex-state ring to the spin-polarized current has hysteretic behavior with
the reasonable values of the thresholds current densities: ignition threshold
is about $10^{8} \text{A}\text{cm}^{-2}$, and elimination current to maintain
the oscillations has much lower values about $10^{6} \text{A} \text{cm}^{-2}$.
The output signal can be extracted by the help of the inverse spin Hall effect
or by the giant magnetoresistance. The output electromotive force averaged over
all sample vanishes, and we suggest to use a ferromagnetic ring or disk in a
vortex state as a GMR analyzer. For an inverse spin Hall analyser we advise to
use two heavy metals with different signs of Spin-Hall angle. The ring-based
STNO is supposed to increase the areas of practical application of the STNOs.
