Dilworth's principal elements (Q1272224)

By \textit{R. P. Dilworth,} an element \(e\) of a multiplicative lattice is called principal if it satisfies the identifies \(a\wedge be=\big ((a:e)\wedge b\big)e\) and \(a\vee (b: e)=(ae\vee b):e.\) Principal elements in multiplicative lattices are the analogue of principal ideals in (commutative) rings. New results regarding principal elements are obtained in the paper; some earlier ones are extended. Applications to ring ideals are given. In addition, the paper contains a number of open problem and a fairly extensive bibliography on principal elements.