Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K\"unneth Splittings and Classification of C*-Algebras with Finitely
  Many Ideals   The class of AD algebras of real rank zero is classified by an exact sequence
of K-groups with coefficients, equipped with certain order structures. Such a
sequence is always split, and one may ask why, then, the middle group is
relevant for classification. The answer is that the splitting map can not
always be chosen to respect the order structures involved.
  This may be rephrased in terms of the ideals of the C*-algebras in question.
We prove that when the C*-algebra has only finitely many ideals, a splitting
map respecting these always exists. Hence AD algebras of real rank zero with
finitely many ideals are classified by (classical) ordered K-theory. We also
indicate how the methods generalize to the full class of ASH algebras with slow
dimension growth and real rank zero.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an