Abstract
Let R be a commutative ring with unity. The notion of almost -integrally closed ring is introduced which generalizes the concept of almost integrally closed domain. Let be the set of all rings such that is a divided prime ideal of R and is a ring homomorphism defined as for all . A ring is said to be an almost -integrally closed ring if is integrally closed in for each nonnil prime ideal of R. Using the idealization theory of Nagata, examples are also given to strengthen the concept.
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