(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2016)
As a consequence of Cohen’s structure Theorem for complete local rings that every _nite commutative ring R of characteristic pn contains a unique special primary subring R0 satisfying R/J(R) = R0/pR0: Cohen called R0 the coe_cient subring of R. In this paper we will study the case when the ring is a transcendental extension local artinian duo ring R; we proved that even in this case R will has a commutative coe_cient subring.