https://wiki.tiffa.net/w/index.php?action=history&feed=atom&title=Item%3AQ6184 2026-04-20T13:42:21Z Revision history for this page on the wiki MediaWiki 1.43.0 https://wiki.tiffa.net/w/index.php?title=Item:Q6184&diff=28285&oldid=prev 2023-03-31T11:20:49Z

<p>‎<span dir="auto"><span class="autocomment">Created claim: </span></span> <a href="/wiki/Property:P14" title="‎has quality‎ | ‎the entity has an inherent or distinguishing non-material characteristic. use a more-specific property when possible‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">has quality</span> <span class="wb-itemlink-id">(P14)</span></span></a>: <a href="/wiki/Item:Q6186" title="‎ascending chain condition‎ | ‎condition in commutative algebra‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">ascending chain condition</span> <span class="wb-itemlink-id">(Q6186)</span></span></a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:20, 31 March 2023</td> </tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P14" href="/wiki/Property:P14">has quality</a></td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span><a title="Item:Q6186" href="/wiki/Item:Q6186">ascending chain condition</a></span></ins></div></td></tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P14" href="/wiki/Property:P14">has quality</a>: <a title="Item:Q6186" href="/wiki/Item:Q6186">ascending chain condition</a> / rank</td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span>Normal rank</span></ins></div></td></tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P14" href="/wiki/Property:P14">has quality</a>: <a title="Item:Q6186" href="/wiki/Item:Q6186">ascending chain condition</a> / qualifier</td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span><a title="Property:P13" href="/wiki/Property:P13">of</a>: <a title="Item:Q6188" href="/wiki/Item:Q6188">ideal</a></span></ins></div></td></tr></table>

Fire https://wiki.tiffa.net/w/index.php?title=Item:Q6184&diff=28274&oldid=prev 2023-03-31T11:17:09Z

<p>‎<span dir="auto"><span class="autocomment">Created claim: </span></span> <a href="/wiki/Property:P333" title="‎defining formula‎ | ‎mathematical formula representing a theorem or law. Maximum length: 400 characters‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">defining formula</span> <span class="wb-itemlink-id">(P333)</span></span></a>: I_1\subseteq\cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq\cdots</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:17, 31 March 2023</td> </tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P333" href="/wiki/Property:P333">defining formula</a></td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span><h4 class="wb-details wb-math-details wb-math-rendered"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{1}\subseteq \cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq \cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <mo>&#x22EF;<!-- ⋯ --></mo> <mo>&#x2286;<!-- ⊆ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>&#x2212;<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <mo>&#x22EF;<!-- ⋯ --></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{1}\subseteq \cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq \cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c4ec2b17cea4dfd94e76e1123018bceb3df5a39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.553ex; height:2.509ex;" alt="{\displaystyle I_{1}\subseteq \cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq \cdots }"></span></h4><div class="wb-details wb-math-details"><code>I_1\subseteq\cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq\cdots</code></div></span></ins></div></td></tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P333" href="/wiki/Property:P333">defining formula</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{1}\subseteq \cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq \cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <mo>&#x22EF;<!-- ⋯ --></mo> <mo>&#x2286;<!-- ⊆ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>&#x2212;<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&#x2286;<!-- ⊆ --></mo> <mo>&#x22EF;<!-- ⋯ --></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{1}\subseteq \cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq \cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c4ec2b17cea4dfd94e76e1123018bceb3df5a39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.553ex; height:2.509ex;" alt="{\displaystyle I_{1}\subseteq \cdots \subseteq I_{k-1}\subseteq I_{k}\subseteq I_{k+1}\subseteq \cdots }"></span> / rank</td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span>Normal rank</span></ins></div></td></tr></table>

Fire https://wiki.tiffa.net/w/index.php?title=Item:Q6184&diff=28273&oldid=prev 2023-03-31T11:16:55Z

<p>‎<span dir="auto"><span class="autocomment">Created claim: </span></span> <a href="/wiki/Property:P1" title="‎subclass of‎ | ‎this item is a subclass (subset) of that item; all instances of these items are instances of those items; different from P2 (instance of), e.g.: K2 is an instance of mountain; volcano is a subclass of mountain (and an instance of volcanic landform).‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">subclass of</span> <span class="wb-itemlink-id">(P1)</span></span></a>: <a href="/wiki/Item:Q6185" title="‎Noetherian module‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">Noetherian module</span> <span class="wb-itemlink-id">(Q6185)</span></span></a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:16, 31 March 2023</td> </tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P1" href="/wiki/Property:P1">subclass of</a></td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span><a title="Item:Q6185" href="/wiki/Item:Q6185">Noetherian module</a></span></ins></div></td></tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P1" href="/wiki/Property:P1">subclass of</a>: <a title="Item:Q6185" href="/wiki/Item:Q6185">Noetherian module</a> / rank</td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span>Normal rank</span></ins></div></td></tr></table>

Fire https://wiki.tiffa.net/w/index.php?title=Item:Q6184&diff=28269&oldid=prev 2023-03-31T11:16:07Z

<p>‎<span dir="auto"><span class="autocomment">Created claim: </span></span> <a href="/wiki/Property:P1" title="‎subclass of‎ | ‎this item is a subclass (subset) of that item; all instances of these items are instances of those items; different from P2 (instance of), e.g.: K2 is an instance of mountain; volcano is a subclass of mountain (and an instance of volcanic landform).‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">subclass of</span> <span class="wb-itemlink-id">(P1)</span></span></a>: <a href="/wiki/Item:Q1345" title="‎ring‎ | ‎algebraic structure in mathematics, not necessarily with multiplicative identity‎"><span class="wb-itemlink"><span class="wb-itemlink-label" lang="en" dir="ltr">ring</span> <span class="wb-itemlink-id">(Q1345)</span></span></a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:16, 31 March 2023</td> </tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P1" href="/wiki/Property:P1">subclass of</a></td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span><a title="Item:Q1345" href="/wiki/Item:Q1345">ring</a></span></ins></div></td></tr><tr><td colspan="2" class="diff-lineno"></td><td colspan="2" class="diff-lineno">Property / <a title="Property:P1" href="/wiki/Property:P1">subclass of</a>: <a title="Item:Q1345" href="/wiki/Item:Q1345">ring</a> / rank</td></tr><tr><td colspan="2"> </td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span>Normal rank</span></ins></div></td></tr></table>

Fire https://wiki.tiffa.net/w/index.php?title=Item:Q6184&diff=28268&oldid=prev 2023-03-31T11:15:59Z

<p>‎<span dir="auto"><span class="autocomment">Created a new Item: </span></span> noetherian ring, algebraic structure</p> <a href="https://wiki.tiffa.net/w/index.php?title=Item:Q6184&amp;diff=28268">Show changes</a>

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