Infinitely Distributive Elements in Posets

Vera Lazarević, Andreja Tepavčević

Infinitely distributive and codistributive elements in posets are studied. It is proved that an element a in a poset P has these properties if and only if the image of a has the corresponding properties in the Dedekind MacNeille completion of P. An application of the order theoretical results to a poset of weak congruences is presented.