The automorphism group of a function lattice: A problem of Jnsson and McKenzie
نویسنده
چکیده
It is shown that Aut(L ~ is naturally isomorphic to Aut(L) x Aut(Q) when L is a directly and exponentially indecomposable lattice, Q a non-empty connected poset, and one of the following holds: Q is arbitrary but L is a jm-lattice, Q is finitely factorable and L is complete with a join-dense subset of completely join-irreducible elements, or L is arbitrary but Q is finite. A problem of J6nsson and McKenzie is thereby solved. Sharp conditions are found guaranteeing the injectivity of the natural map vp.Q from Aut(P) x Aut(Q) to Aut(P ~ (P and Q posets), correcting misstatements made by previous authors. It is proven that, for a bounded poset P and arbitrary Q, the Dedekind-MacNeille completion of P o, DM(P Q), is isomorphic to DM(P)Q. This isomorphism is used to prove that the natural map Vp.Q is an isomorphism if VDM(p),Q is, reducing a poset problem to a more tractable lattice problem.
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