  A finite Grobner-Shirshov basis is constructed for the plactic algebra of
rank 3 over a field K. It is also shown that plactic algebras of rank exceeding
3 do not have finite Grobner-Shirshov bases associated to the natural
degree-lexicographic ordering on the corresponding free algebra. The latter is
in contrast with the case of a strongly related class of algebras, called
Chinese algebras, recently considered by Chen Yuqun and Qiu Jianjun.
