https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Strictly_multiplicatively_monotone_normStrictly multiplicatively monotone norm - Revision history2026-10-08T10:26:53ZRevision history for this page on the wikiMediaWiki 1.41.2https://commalg.subwiki.org/w/index.php?title=Strictly_multiplicatively_monotone_norm&diff=1893&oldid=prevVipul: New page: {{wikilocal}} {{curing-norm property}} ==Definition== A '''strictly multiplicatively monotone norm''' on a commutative unital ring <math>R</math> is a function <math>N: R \setminus \{ 0 ...2009-01-31T22:17:58Z<p>New page: {{wikilocal}} {{curing-norm property}} ==Definition== A '''strictly multiplicatively monotone norm''' on a commutative unital ring <math>R</math> is a function <math>N: R \setminus \{ 0 ...</p>
<p><b>New page</b></p><div>{{wikilocal}}<br />
{{curing-norm property}}<br />
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==Definition==<br />
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A '''strictly multiplicatively monotone norm''' on a commutative unital ring <math>R</math> is a function <math>N: R \setminus \{ 0 \} \to \mathbb{N}_0</math> such that:<br />
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* For <math>ab \ne 0</math>, <math>N(ab) \ge \max \{ N(a), N(b) \}</math>.<br />
* For <math>ab \ne 0</math>, <math>N(ab) = N(a)</math> if and only if <math>a</math> and <math>ab</math> are [[defining ingredient::associate element]]s.<br />
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==Facts==<br />
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* [[Strictly multiplicatively monotone norm on Bezout domain is a Dedekind-Hasse norm]]</div>Vipul