Minimal Spectrum and the Radical of Chinese Algebras

Abstract

It is shown that every minimal prime ideal of the Chinese algebra of any finite rank is generated by a finite set of homogeneous elements of degree 2 or 3. A constructive way of producing minimal generating sets of all such ideals is found. As a consequence, it is shown that the Jacobson radical of the Chinese algebra is nilpotent. Moreover, the radical is not finitely generated if the rank of the algebra exceeds 2.