Very basic question about localizations Let A be a ring, S a multiplicatively closed subset. Is it true that a1∈S−1A is a non zero-divisor if and only if a∈A is?

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Very basic question about localizations  Let A be a ring, S a multiplicatively closed subset. Is it true that a1∈S−1A is a non zero-divisor if and only if a∈A is?

uporabah5pn · Accepted Answer

Set A=Z6 and S=A3Z6. Then 2^ is a zerodivisor in A and 2^1^ is not zerodivisor in S−1A. (Actually it is invertible in S−1A.)

Very basic question about localizations Let A be a ring, S a multiplicatively closed subset....

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