We report results on the rectification properties of a carbon nanotube (CNT) ring transistor, contacted by CNT leads, whose novel features have been recently communicated by Watanabe et al. [Appl. Phys. Lett. 78, 2928 (2001)]. This paper contains results which are validated by the experimental observations. Moreover, we report on additional features of the transmission of this ring device which are associated with the possibility of breaking the lead inversion symmetry. The linear conductance displays a ``chessboard''-like behavior alternated with anomalous zero-lines which should be directly observable in experiments. We are also able to discriminate in our results structural properties (quasi-onedimensional confinement) from pure topological effects (ring configuration), thus helping to gain physical intuition on the rich ring phenomenology.