Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combined Algebraic Properties in Gaussian and Quaternion Ring   It is known that for an IP^{*} set A in (\mathbb{N},+) and a sequence
\left\langle x_{n}\right\rangle _{n=1}^{\infty} in \mathbb{N}, there exists a
sum subsystem \left\langle y_{n}\right\rangle _{n=1}^{\infty} of \left\langle
x_{n}\right\rangle _{n=1}^{\infty} such that FS\left(\left\langle
y_{n}\right\rangle _{n=1}^{\infty}\right)\cup FP\left(\left\langle
y_{n}\right\rangle _{n=1}^{\infty}\right)\subseteq A. Similar types of results
have also been proved for central^{*} sets and C^{*}-sets where the sequences
have been considered from the class of minimal sequences and almost minimal
sequences. In this present work, our aim to establish the similar type of
results for the ring of Gaussian integers and the ring of integer quaternions.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys