# Algebra Seminar talk

2016-04-15

Helmut **Länger***Relatively pseudocomplemented posets*

Abstract:

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.