Rigid extensions of algebraic frames
Tóm tắt
An extension G ≤ H of lattice-ordered groups is said to be a rigid extension if for each
$${h \in H}$$
there exists a
$${g \in G}$$
such that h
⊥⊥ = g
⊥⊥. In this paper, we will define rigid extensions and some other generalizations in the context of algebraic frames satisfying the FIP. One of the main results is a characterization of rigid extensions using d-elements of the frame. We also show that a rigid extension between two algebraic frames satisfying the FIP will induce a homeomorphism between their corresponding minimal prime spaces with respect to both the hull-kernel topology and the inverse topology. Moreover, basic open sets map to basic open sets.
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