Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Catenarity in quantum nilpotent algebras   In this paper, it is established that quantum nilpotent algebras (also known
as CGL extensions) are catenary, i.e., all saturated chains of inclusions of
prime ideals between any two given prime ideals $P \subsetneq Q$ have the same
length. This is achieved by proving that the prime spectra of these algebras
have normal separation, and then establishing the mild homological conditions
necessary to apply a result of Lenagan and the first author. The work also
recovers the Tauvel height formula for quantum nilpotent algebras, a result
that was first obtained by Lenagan and the authors through a different
approach.

28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys