Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sets of Lengths   Oftentimes the elements of a ring or semigroup $H$ can be written as finite
products of irreducible elements, say $a=u_1 \cdot \ldots \cdot u_k = v_1 \cdot
\ldots \cdot v_{\ell}$, where the number of irreducible factors is distinct.
The set $\mathsf L (a) \subset \mathbb N$ of all possible factorization lengths
of $a$ is called the set of lengths of $a$, and the full system $\mathcal L (H)
= \{ \mathsf L (a) \mid a \in H \}$ is a well-studied means of describing the
non-uniqueness of factorizations of $H$. We provide a friendly introduction,
which is largely self-contained, to what is known about systems of sets of
lengths for rings of integers of algebraic number fields and for transfer Krull
monoids of finite type as their generalization.

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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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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: bayes-an
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The categories of this paper are: dg-ga
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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: astro-ph
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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: solv-int