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A note on zero-divisors of commutative ringsDOI: 10.1007/s40065-012-0003-8 Abstract: In this paper we show that if a ring R has finite Goldie dimension, then every finitely generated ideal of R consisting of zero-divisors has non-zero annihilator. We also construct an example of a ring of infinite Goldie dimension such that above condition does not hold.
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