Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On additivity of local entropy under flat extensions   Let $f\colon(R,\mathfrak{m})\rightarrow S$ be a local homomorphism of
Noetherian local rings. Consider two endomorphisms \textit{of finite length}
(i.e., with zero-dimensional closed fibers) $\varphi\colon R\rightarrow R$ and
$\psi\colon S\rightarrow S$, satisfying $\psi\circ f=f\circ\varphi$. Then
$\psi$ induces a finite length endomorphism $\overline{\psi}\colon
S/f(\mathfrak{m})S\rightarrow S/f(\mathfrak{m})S$. When $f$ is flat, under the
assumption that $S$ is Cohen-Macaulay we prove an additivity formula:
$h_{\mathrm{loc}}(\psi)=h_{\mathrm{loc}}(\varphi)+h_{\mathrm{loc}}(\overline{\psi})$
for \textit{local entropy}.

27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys