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Dilworth’s principal elements. (English) Zbl 0901.06013

By 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.
Reviewer: J.Duda (Brno)

MSC:

06F10 Noether lattices
16P40 Noetherian rings and modules (associative rings and algebras)
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