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On the Complete Ring of Quotients
Published online by Cambridge University Press: 20 November 2018
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In [2: p. 415], P. Gabriel proves that if R is a ring with 1 and S is a non-empty multiplicative set such that 0∉S, then S-1R exists if and only if for every pair (a, s)∈R×S, there is a pair (b, t)∈R×S such that at=sb and if s1a=0 for some s1 in S then as2=0 for some s2 in S. The purpose of this note is to give a self contained elementary proof of Gabriel’s result.
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- Copyright © Canadian Mathematical Society 1974
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