عنوان مجله
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JOURNAL OF PURE AND APPLIED ALGEBRA
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چکیده
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In this article, we investigate the avoidance property of ideals and rings. Among the
main results, a general version of the avoidance lemma is formulated. It is shown that
every idempotent ideal (and hence every pure ideal) has avoidance. The avoidance
property of arbitrary direct products of avoidance rings is characterized. It is shown
that every overing of an avoidance domain is an avoidance domain. Next, we show
that every avoidance N-graded ring whose base subring is a finite field is a PIR. It is
also proved that the avoidance property is preserved under flat ring epimorphisms.
Dually, we formulate a notion of strong avoidance, and show that it is reflected by
pure morphisms.
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