Chajda, I., Kolařík, M., & Länger, H. (2024). c-ideals in complemented posets. Mathematica Bohemica, 149(3), 305–316. https://doi.org/10.21136/MB.2023.0108-22
In their recent paper on posets with a pseudocomplementation denoted by ∗ the first and the third author introduced the concept of a ∗-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.