Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebras of Reduced $E$-Fountain Semigroups and the Generalized Ample
  Identity   Let $S$ be a reduced $E$-Fountain semigroup. If $S$ satisfies the congruence
condition, there is a natural construction of a category $\mathcal{C}$
associated with $S$. We define a $\Bbbk$-module homomorphism $\varphi:\Bbbk
S\to\Bbbk\mathcal{C}$ (where $\Bbbk$ is any unital commutative ring). With some
assumptions, we prove that $\varphi$ is an isomorphism of $\Bbbk$-algebras if
and only if some weak form of the right ample identity holds in $S$. This gives
a unified generalization for a result of the author on right restriction
$E$-Ehresmann semigroups and a result of Margolis and Steinberg on the Catalan
monoid.

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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph