Vol. 89, No. 1, 1980

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Krull rings

Robert Edward Kennedy

Vol. 89 (1980), No. 1, 131–136

We extend the notion of a Krull domain to commutative rings with identity which may contain zero divisors. In order to do this we present a definition of the divisors of an arbitrary ring, and show that the collection of divisors is a commutative semigroup with identity and is a group if and only if the ring is completely integrally closed. In addition, an extension of unique factorization domains to arbitrary commutative rings is used to investigate the relationship between Krull rings and unique factorization rings. In particular, it is shown that a unique factorization ring is a Krull ring with trivial class group.

Mathematical Subject Classification 2000
Primary: 13F15
Received: 16 February 1979
Published: 1 July 1980
Robert Edward Kennedy