P-NOETHERIAN INTEGRAL DOMAINS WITH 1 IN THE STABLE RANGE
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P-NOETHERIAN INTEGRAL DOMAINS WITH 1 IN THE STABLE RANGE
collection of maximal ideals of R containing A and /= {ideals A of. R I JiA) =A}. We say that R is /-noetherian if the ideals of / satisfy the ascending chain condition.
P-NOETHERIAN INTEGRAL DOMAINS WITH 1 IN THE STABLE RANGE WILLIAM J. HEINZER
Let R be a commutative ring with identity. In [l, p. 29], Bass has shown that if the maximal spectrum of R is noetherian of combinatorial dimension d and if R' is a finite P-algebra, then d + 1 defines a stable range for GL(P'). Estes and Ohm in [2] have considered some topics related to Bass's theorem mainly for the case when R' =P. In particular, they prove, for any integer n^O, the existence of an integral domain D such that the maximal spectrum of D has dimension n and 1 is in the stable range of D. They raise the question of whether there exists a domain D with these properties for which the maximal spectrum of D is noetherian. Our purpose is to give an affirmative answer to this question. If A is an ideal of P then we let JiA) denote the intersection of the collection of maximal ideals of R containing A and /= {ideals A of
R I JiA) =A}. We say that R is /-noetherian
if the ideals of / satisfy
the ascending chain condition. This is equivalent to the statement that the maximal spectrum of R is noetherian. The dimension of the maximal spectrum of R is n provided there is a chain P0
