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The purity of a completion
1976
Glasgow Mathematical Journal
This note establishes two statements from R. M. Fossum's review [1] of a paper by E. A. Magarian [2] . Firstly, if A -» B is a pure homomorphism (of commutative rings) then A [[x u ..., x s ]]-*B [[x lt ...,x s ]] is pure. Secondly, if R n -*R is a directed family of pure homomorphisms then \jR n -+ R is pure. A consequence is that if R n -> R is a directed family of pure homomorphisms and if R is Noetherian, then uR n [[x t , ..., x s ]] is Noetherian. A homomorphism A -> B is said to be pure
doi:10.1017/s0017089500002846
fatcat:7426mflswfdvxj4mu3tcotafoa