Jump to navigation Jump to search

General

Display information for equation id:math.245723.0 on revision:245723

* Page found: Socle (mathematics) (eq math.245723.0)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: f8b0c26cff6e2f3cf43a6f376258a88d

TeX (original user input):

\mathrm {soc}(M) = \sum \{ N \mid N \text{ is a simple submodule of }M \}. \,

LaTeXML (experimental; uses MathML) rendering

MathML (3.862 KB / 863 B) :

soc ( M ) = { N N  is a simple submodule of  M } . soc 𝑀 conditional-set 𝑁 𝑁  is a simple submodule of  𝑀 {\displaystyle{\mathrm{soc}}(M)=\sum\{N\mid N{\text{ is a simple submodule of % }}M\}.\,}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\mathrm{soc}}(M)=\sum\{N\mid N{\text{ is a simple submodule of %&#10;}}M\}.\,}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.2.cmml">
      <mrow id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">
        <mrow id="p1.1.m1.1.18.2.1" xref="p1.1.m1.1.18.2.1.cmml">
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">soc</mi>
          <mo id="p1.1.m1.1.18.2.1.1" xref="p1.1.m1.1.18.2.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.18.2.1.2" xref="p1.1.m1.1.18.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.18.2.1.cmml">(</mo>
            <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">M</mi>
            <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.18.2.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.18.2.2" xref="p1.1.m1.1.18.2.2.cmml">
          <mrow id="p1.1.m1.1.18.2.2a" xref="p1.1.m1.1.18.2.2.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml"></mo>
            <mrow id="p1.1.m1.1.18.2.2.1" xref="p1.1.m1.1.18.2.2.1.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.18.2.2.1.1.1.cmml">{</mo>
              <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">N</mi>
              <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.18.2.2.1.1.1.cmml"></mo>
              <mrow id="p1.1.m1.1.18.2.2.1.2" xref="p1.1.m1.1.18.2.2.1.2.cmml">
                <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">N</mi>
                <mo id="p1.1.m1.1.18.2.2.1.2.1" xref="p1.1.m1.1.18.2.2.1.2.1.cmml"></mo>
                <mtext id="p1.1.m1.1.13" xref="p1.1.m1.1.13a.cmml"> is a simple submodule of </mtext>
                <mo id="p1.1.m1.1.18.2.2.1.2.1a" xref="p1.1.m1.1.18.2.2.1.2.1.cmml"></mo>
                <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">M</mi>
              </mrow>
              <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.18.2.2.1.1.1.cmml">}</mo>
            </mrow>
          </mrow>
        </mstyle>
      </mrow>
      <mo rspace="4.2pt" id="p1.1.m1.1.16" xref="p1.1.m1.1.18.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18">
        <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
        <apply id="p1.1.m1.1.18.2.1.cmml" xref="p1.1.m1.1.18.2.1">
          <times id="p1.1.m1.1.18.2.1.1.cmml" xref="p1.1.m1.1.18.2.1.1"/>
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">soc</ci>
          <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑀</ci>
        </apply>
        <apply id="p1.1.m1.1.18.2.2.cmml" xref="p1.1.m1.1.18.2.2">
          <sum id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
          <apply id="p1.1.m1.1.18.2.2.1.1.cmml" xref="p1.1.m1.1.18.2.2.1">
            <csymbol cd="latexml" id="p1.1.m1.1.18.2.2.1.1.1.cmml" xref="p1.1.m1.1.9">conditional-set</csymbol>
            <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑁</ci>
            <apply id="p1.1.m1.1.18.2.2.1.2.cmml" xref="p1.1.m1.1.18.2.2.1.2">
              <times id="p1.1.m1.1.18.2.2.1.2.1.cmml" xref="p1.1.m1.1.18.2.2.1.2.1"/>
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑁</ci>
              <ci id="p1.1.m1.1.13a.cmml" xref="p1.1.m1.1.13">
                <mtext id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"> is a simple submodule of </mtext>
              </ci>
              <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑀</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\mathrm{soc}}(M)=\sum\{N\mid N{\text{ is a simple submodule of %
}}M\}.\,}</annotation>
  </semantics>
</math>

SVG (15.181 KB / 5.985 KB) :

s o c times left-parenthesis upper M right-parenthesis equals sigma-summation left-brace upper N bar upper N times is a simple submodule of times upper M right-brace period

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (1.138 KB / 445 B) :

s o c ( M ) = { N N  is a simple submodule of  M } . {\displaystyle \mathrm {soc} (M)=\sum \{N\mid N{\text{ is a simple submodule of }}M\}.\,}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathrm {soc} (M)=\sum \{N\mid N{\text{ is a simple submodule of }}M\}.\,}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="normal">s</mi>
          <mi mathvariant="normal">o</mi>
          <mi mathvariant="normal">c</mi>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>M</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mo>&#x2211;<!-- ∑ --></mo>
        <mo fence="false" stretchy="false">{</mo>
        <mi>N</mi>
        <mo>&#x2223;<!-- ∣ --></mo>
        <mi>N</mi>
        <mrow class="MJX-TeXAtom-ORD">
          <mtext>&#xA0;is a simple submodule of&#xA0;</mtext>
        </mrow>
        <mi>M</mi>
        <mo fence="false" stretchy="false">}</mo>
        <mo>.</mo>
        <mspace width="thinmathspace" />
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \mathrm {soc} (M)=\sum \{N\mid N{\text{ is a simple submodule of }}M\}.\,}</annotation>
  </semantics>
</math>

SVG (13.584 KB / 5.741 KB) :

{\displaystyle \mathrm {soc} (M)=\sum \{N\mid N{\text{ is a simple submodule of }}M\}.\,}

PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Socle (mathematics) page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results