. It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid. It was first noticed by L. Skula  that a domain R is a Krull domain if and only if the multiplicative monoid R n f0g is a Krull monoid (or, equivalently, admits a divisor theory). For independent proofs and historical remarks see  and . In this note we extend the above-mentioned result to Krull rings with zero divisors as treated in . All rings in this note are commutative and possess a unit element. If R is a ring, we denote by R ffl the monoid of regular elements of R , by R \Theta the group of invertible elements of R and by T (R) a total quotient ring of R ; clearly, T (R) ffl = T (R) \Theta . For a prime ideal P of R , we set R (P ) = (R ffl n P ) \Gamma1 R ae T (R) . Throughout, we shall assume that R is a Marot ring, and we shall use the Marot property in the following form. Lemma. A ring R is a Marot ring if and only if the following cond..
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