Idempotent Noether lattices
Kenneth P. Bogart · Proceedings of the American Mathematical Society · 1969
In his paper, Abstract commutative ideal theory [2 ], Dilworth proved that a Noether lattice on which the multiplication is the meet operation is a finite Boolean algebra. This note proves that if the multiplication in a Noether lattice is idempotent (A2= A for all A in the lattice), then the lattice is a finite Boolean algebra. In a Noether lattice the term maximal element refers to a maximal nonidentity element (i.e. a coatom).