https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Filtrative_norm 2026-11-02T23:31:43Z Revision history for this page on the wiki MediaWiki 1.41.2 https://commalg.subwiki.org/w/index.php?title=Filtrative_norm&diff=1853&oldid=prev 2009-01-24T01:17:20Z

<p>New page: {{curing-norm property}} ==Definition== A <a href="/wiki/Norm_on_a_commutative_unital_ring" title="Norm on a commutative unital ring">norm on a commutative unital ring</a> is termed &#039;&#039;&#039;filtrative&#039;&#039;&#039; if it is a function from the nonzero elements of the ring to &#039;&#039;nonnegative&#039;&#039; in...</p> <p><b>New page</b></p><div>{{curing-norm property}}<br /> <br /> ==Definition==<br /> <br /> A [[norm on a commutative unital ring]] is termed &#039;&#039;&#039;filtrative&#039;&#039;&#039; if it is a function from the nonzero elements of the ring to &#039;&#039;nonnegative&#039;&#039; integers, and further, for any natural number &lt;math&gt;n&lt;/math&gt;, the set of elements with norm less than &lt;math&gt;n&lt;/math&gt;, along with zero, form an additive subgroup of the ring.<br /> <br /> ==Relation with other properties==<br /> <br /> ===Stronger properties===<br /> <br /> * [[Weaker than::Filtrative Euclidean norm]]</div>

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