On A Certain Krull Symmetry Of a Noetherian Ring

Abstract

In this note we show that if a noetherian ring R is left and right Krull-homogenous and if: \Lambda ={P\textexclamdown {\epsilon} spec.R/ |R/P\textexclamdown|_r =|R|_r} and v ={Qj {\epsilon} spec.R| |R/Qj|l=|R|l} and P =\cap P\textexclamdown{\epsilon} \Lambda P\textexclamdown and Q = \cap Qj{\epsilon}VQj then the following hold true; (1) Pn =0, for some integer n\geq1 (2) \Lambda =v