TY - JOUR
AU1 - Walker, R.
AB - LOCAL RINGS AND NORMALIZING SETS OF ELEMENTS By R. WALKER [Received 19 March 1971] Throughout this paper, all the rings considered will be associative rings with identity elements. If / is an ideal of a ring B, we denote by ^(I) the set {x e B | x +1 is regular in B/I). If P is a prime ideal of B, we say that localization at P is classical if we can form the right quotient ring of B with respect to ^(P), and we denote this ring by B . It is well known that, if B is right noetherian and has the right Ore condition with respect to #(P), then the ring B can be con- structed and B is a right noetherian ring with a unique maximal ideal M such that M is the Jacobson radical of B and B. /M is an artinian p p simple ring (see [4] Ch. 5). An ideal / of a ring B is said to have the AB-property if, for any right ideal J of B, there exists n such that Jnl c: JI. In §1, we obtain a change-of-rings theorem involving the Krull dimension as defined in [12]. 
TI - Local Rings and Normalizing Sets of Elements
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-24.1.27
DA - 1972-02-01
UR - https://www.deepdyve.com/lp/wiley/local-rings-and-normalizing-sets-of-elements-mnLg0lVYPx
SP - 27
EP - 45
VL - s3-24
IS - 1
DP - DeepDyve
ER -