ON THE SECOND LAYER CONDITION IN FINITE EXTENSIONS

Abstract

The transfer of the right (strong) second layer condition from a Noetherian ring R to a module finite extension ring S is investigated. An affirmative result for S a strongly group-graded ring (with finite underlying group) is generalized to include any module finite extension. Also, it is determined when tameness is preserved in passing between R-modules and S-modules and a positive result in either direction is given when the appropriate ring satisfies the right second layer condition. An important tool used to obtain these results is used to show that if R satisfies the right second layer condition, then Lying Over holds without any need to assume that S satisfies the second layer condition on either side.