Relatively pseudocomplemented posets

Relatively pseudocomplemented posets

Blog Article

We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets.We show some properties of the PV Inverter binary operation of relative pseudocomplementation and provide some corresponding characterizations.We show that relatively pseudocomplemented posets satisfying a certain simple identity in Cover Right two variables are join-semilattices.Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain condition and one more natural condition.

Suitable examples are provided.