Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative projectivity and transferability for partial lattices   A partial lattice P is ideal-projective, with respect to a class C of
lattices, if for every K $\in$ C and every homomorphism $\phi$ of partial
lattices from P to the ideal lattice of K, there are arbitrarily large choice
functions f : P $\rightarrow$ K for $\phi$ that are also homomorphisms of
partial lattices. This extends the traditional concept of (sharp)
transferability of a lattice with respect to C. We prove the following: (1) A
finite lattice P, belonging to a variety V, is sharply transferable with
respect to V iff it is projective with respect to V and weakly distributive
lattice homomorphisms, iff it is ideal-projective with respect to V. (2) Every
finite distributive lattice is sharply transferable with respect to the class R
mod of all relatively complemented modular lattices. (3) The gluing D 4 of two
squares, the top of one being identified with the bottom of the other one, is
sharply transferable with respect to a variety V iff V is contained in the
variety M$\omega$ generated by all lattices of length 2. (4) D 4 is projective,
but not ideal-projective, with respect to R mod. (5) D 4 is transferable, but
not sharply transferable, with respect to the variety M of all modular
lattices. This solves a 1978 problem of G. Gr\"atzer. (6) We construct a
modular lattice whose canonical embedding into its ideal lattice is not pure.
This solves a 1974 problem of E. Nelson.

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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat