The notion of principal element of a commutative multiplicative lattice was introduced by Dilworth. In this note the principal elements of the lattice of ideals of a commutative ring with unity R are characterized as those ideals of R which are finitely generated and locally principal ideals. It follows that a regular ideal of R is a principal element of the lattice of ideals of R if and only if it is invertible. In [3], Dilworth introduced the notion of principal element of a commutative multiplicative lattice L: an element M of L is a principal element of L if (AC\B:M)M=AMC\B and (AUBM):M=A:MUB for all elements A and B of L. Dilworth showed that a principal ideal of a commutative ring with unity R is a principal element of the lattice L(R) of ideals of R, and he extended the Krull principal ideal theorem to principal elements of a Noether lattice [3, Theorem 6.4]. Throughout this note, let R be a commutative ring with unity. It is natural to ask which ideals of R are principal elements of L(R). Dilworth [3, Theorem 7.1 ] showed that if R is a unique factorization domain, then every principal element of L(R) is a principal ideal of R. Bogart [1, Corollary 2.1] and Johnson [8, Corollary 1.5] showed that this is also the case when R is a Noetherian local ring. On the other hand, as Dilworth pointed out, if R is a Dedekind domain, then every ideal of R is a principal element of L(R). Janowitz [7] determined those rings which have this property; they are the Noetherian multiplication rings. It is well known that an element of a Noether lattice is principal if and only if it is principal in every localization. This is true of every multiplicative lattice which has a suitable localization theory, i.e., for which the assertion of [9, Proposition 4] holds. Combining this with the result of Bogart and Johnson, we see that if R is a Noetherian ring, then an ideal of R is a principal element of L(R) if and only if Received by the editors September 15, 1970. AMS 1970 subject classifications. Primary 13A15; Secondary 13F05.