On Rings of Fractions Journal Articles uri icon

  •  
  • Overview
  •  
  • Research
  •  
  • Identity
  •  
  • Additional Document Info
  •  
  • View All
  •  

abstract

  • Let R be a commutative Noetherian ring with identity, and let M be a fixed ideal of R. Then, trivially, ring multiplication is continuous in the ilf-adic topology. Let S be a multiplicative system in R, and let j = js: R → S-1R, be the natural map. One can then ask whether (cf. Warner [3, p. 165]) S-1R is a topological ring in ihe j(M)-adic topology. In Proposition 1, I prove this is the case if and only if M ⊂ p(S), whereHence S-1R is a topological ring for all S if and only if M ⊂ p*(R), where

publication date

  • December 1970