M. Filipowicz, Marek Kȩpczyk
Abstract
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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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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.
Key concepts: Mathematics, Annihilator, Zero (linguistics), Zero divisor, Dimension (graph theory), Commutative ring, Ideal (ethics), Ring (chemistry)