Coz-onto Frame Maps and Some Applications

A frame homomorphism is coz-onto if it maps the cozero part of its domain surjectively onto that of its codomain. This captures the notion of a z-embedded subspace of a topological space in a point-free setting. We give three different types of characterizations of coz-onto homomorphisms. The first is in terms of elements, the second in terms of quotients, and the last in terms of ideals. As an application of properties of coz-onto homomorphisms developed herein, we present some characterizations of $F$ - and $F^{prime }$ -frames.