%0 Journal Article
%T <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <mstyle mathvariant='bold' mathsize='normal'><mi>K</mi></mstyle><msup>   <mi>&#x2124;</mi>   <mrow>    <mrow><mo>(</mo>     <mstyle mathvariant='bold' mathsize='normal'><mi>n</mi></mstyle>    <mo>)</mo></mrow></mrow>  </msup>  </mrow></math>上分次扩张的子环<br>Subrings of Graded Extensions in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <mstyle mathvariant='bold' mathsize='normal'><mi>K</mi></mstyle><msup>   <mi>&#x2124;</mi>   <mrow>    <mrow><mo>(</mo>     <mstyle mathvariant='bold' mathsize='normal'><mi>n</mi></mstyle>    <mo>)</mo></mrow></mrow>  </msup>  </mrow></math>
%A 陆修灿
%J Pure Mathematics
%P 93-97
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.152050
%X 斜群环是一类非常重要的环&#65292;其上的分次扩张是一类非常重要的环扩张。本文在<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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上分次扩张的基础下&#65292;研究了<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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上分次扩张的子环&#65292;利用锥的理论证明了<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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上分次扩张的子环与之相对应的锥的集合有一个一一对应关系。<br>Skew group rings are a very important class of rings, and the graded extensions over them are a very important class of ring extensions. In this paper, based on the graded extensions over <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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, we study the subrings of the graded extensions over <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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  <mstyle mathvariant='bold' mathsize='normal'><mi>K</mi></mstyle><msup>
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    <mrow><mo>(</mo>
     <mstyle mathvariant='bold' mathsize='normal'><mi>n</mi></mstyle>
    <mo>)</mo></mrow></mrow>
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. By using the theory of cones, it is proved that there is a one-to-one correspondence between the set of subrings of the graded extensions over <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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   <mi>&#x2124;</mi>
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    <mrow><mo>(</mo>
     <mstyle mathvariant='bold' mathsize='normal'><mi>n</mi></mstyle>
    <mo>)</mo></mrow></mrow>
  </msup>
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 and the set of corresponding cones.
%K 斜群环&#65292
%K 分次扩张&#65292
%K 子环&#65292
%K 锥<br>Skew Group Rings
%K Graded Extension
%K Subring
%K Cone
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=107999