Some results on abstract commutative ideal theory
The authors establish abstract versions of Nakayama's Lemma and the Krull Intersection Theorem. Using these results, they obtain some equivalent conditions for a multiplicative lattice with 1 compact to be a finite Boolean algebra. Further they study multiplicative lattices in which semiprimary elements are primary. They introduce the concepts of weak \(r\)-lattices and weak \(M\)-lattices. They show that a weak \(r\)-lattice is an \(M\)-lattice if and only if it is a weak \(M\)-lattice. Finally they investigate the lattice of filters of a bounded commutative multiplicative semilattice, and using these they characterize regular lattices.
scientific article; zbMATH DE number 737237
scientific article