Congruence Lattices of Semilattices with Operators
نویسندگان
چکیده
We begin by recalling the general theory of adjoints on finite semilattices. A finite join semilattice with 0 is a lattice, with the naturally induced meet operation. Thus a finite lattice S can be regarded as a semilattice in two ways, either S = 〈S,+, 0〉 or S = 〈S,∧, 1〉. Given a (+, 0)-homomorphism g : S → T , define the adjoint h : T → S by h(t) = ∑ {s ∈ S : gs ≤ t} so that gs ≤ t iff s ≤ ht . Proof. The ⇒ direction is clear. For the resverse, assume s0 ≤ ht. Then gs0 ≤ ght = ∑ {gs : gs ≤ t} ≤ t, as desired.
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ورودعنوان ژورنال:
- Studia Logica
دوره 104 شماره
صفحات -
تاریخ انتشار 2016