Properties of Relational Structures , Posets , Lattices and Maps 1

In the paper we present some auxiliary facts concerning posets and maps between them. Our main purpose, however is to give an account on complete lattices and lattices of ideals. A sufficient condition that a lattice might be complete, the fixed-point theorem and two remarks upon images of complete lattices in monotone maps, introduced in [10, pp. 8–9], can be found in Section 7. Section 8 deals with lattices of ideals. We examine the meet and join of two ideals. In order to show that the lattice of ideals is complete, the infinite intersection of ideals is investigated.