Multiplicative lattices with Noetherian spectrum

الملخص EN

Let R be a commutative ring with identity.

Recall that the ring R has Noetherian spectrum if R satisfies the ascending chain condition for radical ideals.

We say that a multiplicative lattice L has Noetherian spectrum (has property (N)) if L satisfies the ascending chain condition for radical elements.

The purpose of this paper is to study properties equivalent to the property (N) in multiplicative lattices, and to define a multiplicative lattice L which has a locally Noetherian spectrum.

We proved that L has a locally Noetherian spectrum need not have Noetherian spectrum.

So, we characterized those lattices with locally.

Noetherian spectrum which have also Noetherian spectrum.