Algebra Seminar talk

Helmut Länger
Relatively pseudocomplemented posets

We extend the notion of a relative pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relative pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relative 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.