Properties of Relational Structures , Posets , Lattices and Maps 1 Mariusz Żynel
نویسنده
چکیده
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 [9, 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.
منابع مشابه
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 deal...
متن کاملSome results on $L$-complete lattices
The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...
متن کاملMaximal Sublattices of Nite Distributive Lattices
Algebraic properties of lattices of quotients of nite posets are considered. Using the known duality between the category of all nite posets together with all order-preserving maps and the category of all nite distributive (0; 1)-lattices together with all (0; 1)-lattice ho-momorphisms, algebraic and arithmetic properties of maximal proper sublattices and, in particular, Frattini sublattices of...
متن کاملHow to use algebraic structures
Mathematical branches are based on relational and operational structures. These arose in mathematics through orderings, measures, classification, counting and basic operations with numbers. Among relational structures we advance partially ordered sets (posets), lattices and Boolean algebras, the latter satisfying all important ordering properties. These ordered structures appear in nature, and ...
متن کاملGeneral Projections in Spaces of Pencils
The notion of the central projection in spaces of pencils is generalized and new concepts of projections are introduced. The category of projectivities with segment subspaces as objects arises. These general projectivities are collineations given by linear maps. Properties of pencils of segment subspaces and projections between segments are investigated. Classical projections of lines onto penc...
متن کامل