Abstract
Throughout this paper the word ‘ring’ will mean ‘commutative Noetherian ring with non-zero identity’, and A will always denote such a ring. It will only be assumed that A is local when this is explicitly stated, but when this is the case m (resp. k) will always be used to denote the maximal ideal (resp. residue field) of A. It is to be understood that ring homomorphisms respect identity elements.
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