Abstract
We give a short survey of the rationality problem for quasi-monomial actions which includes Noether's problem and the rationality problem for algebraic tori, and report some results on rationality problem in three recent papers Hoshi, Kang and Kitayama [HKKi], Hoshi, Kang and Kunyavskii [HKKu] and Hoshi and Yamasaki [HY].
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