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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Acknowledgments
The authors thank the two referees for their valuable suggestion, which allowed to improve an earlier version of this paper. They also thank Professor Z. Bartosiewicz for calling their attention to the question and Professor E. R. Puczyłowski for his many useful comments on this work. Supported by Bialystok University of Technology Grant No. S/WI/2/11.
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Filipowicz, M., Kȩpczyk, M. A note on zero-divisors of commutative rings. Arab. J. Math. 1, 191–194 (2012). https://doi.org/10.1007/s40065-012-0003-8
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DOI: https://doi.org/10.1007/s40065-012-0003-8