منابع مشابه
Projective Lattices
such that f(g(a)) = a for all a ∈ L. Projective lattices are characterized in [3] by four conditions. This talk will discuss two of them that are of current interest. If g in (2) is only required to be order-preserving, it is called an isotone section of the epimorphism (1). We will characterize which lattices L have an isotope section for every epimorphism (1). We will use this to characterize...
متن کاملOn the Relationship between Projective Distributive Lattices and Boolean Algebras
The main result of this paper is the following theorem: If a projective Boolean algebra B is generated by its sublattice L, then there is a projective distributive lattice D which is a sublattice of L and generates B.
متن کاملProjective Ordinal Sums of Lattices and Isotone Sections
This note gives a complete characterization of when the ordinal sum of two lattices (the lattice obtained by placing the second lattice on top of the first) is projective. This characterization applies not only to the class of all lattices, but to any variety of lattices, and in particular, to the class of distributive lattices. Lattices L with the property that every epimorphism onto L has an ...
متن کاملOrdinal Sums of Projective Lattices and Isotone Sections
A lattice L is projective in a variety V of lattices if whenever f : K L is an epimorphism, there is a homomorphism g : L→ K such that f(g(a)) = a for all a ∈ L. Note g is one-to-one and ρ = gf : K→ K is a retraction of K; that is, ρ is an endomorphism of K and ρ2 = ρ. The sublattice ρ(K) = g(L) of K is isomorphic to L. The image g(L) is a retract of K. In a slight abuse of terminology, we will...
متن کاملLaterally complete and projective hulls of semilinear residuated lattices
The existence of lateral completions of `-groups is an old problem that was first solved, for conditionally complete vector lattices, by Nakano [5]. The existence and uniqueness of lateral completions of representable `-groups was first obtained as a consequence of the orthocompletions of Bernau [1], and later the proofs were simplified by Conrad [3], who also proved the existence and uniquenes...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1978
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1978.75.93