Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When is $\mathfrak{m}:\mathfrak{m}$ an almost Gorenstein ring?   Given a one-dimensional Cohen-Macaulay local ring $(R,\mathfrak{m},k)$, we
prove that it is almost Gorenstein if and only if $\mathfrak{m}$ is a canonical
module of the ring $\mathfrak{m}:\mathfrak{m}$. Then, we generalize this result
by introducing the notions of almost canonical ideal and gAGL ring and by
proving that $R$ is gAGL if and only if $\mathfrak{m}$ is an almost canonical
ideal of $\mathfrak{m}:\mathfrak{m}$. We use this fact to characterize when the
ring $\mathfrak{m}:\mathfrak{m}$ is almost Gorenstein, provided that $R$ has
minimal multiplicity. This is a generalization of a result proved by Chau,
Goto, Kumashiro, and Matsuoka in the case in which $\mathfrak{m}:\mathfrak{m}$
is local and its residue field is isomorphic to $k$.

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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: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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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