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unity of subring
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(Theorem)
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Proof. Because $u$ is not unity of $R$ there exists an element $r$ of $R$ such that $ru \neq r$ Then we have $(ru)u = r(uu) = ru$ which implies that $0 = (ru)u-ru = (ru-r)\cdot u$ Since neither $ru-r$ , nor $u$ , is 0, the element $u$ , is a zero divisor in $R$
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"unity of subring" is owned by pahio.
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Cross-references: implies, proof, zero divisor, unity, non-zero unity, ring, subring
This is version 4 of unity of subring, born on 2004-11-18, modified 2006-03-05.
Object id is 6492, canonical name is UnityOfSubring.
Accessed 1473 times total.
Classification:
| AMS MSC: | 13-00 (Commutative rings and algebras :: General reference works ) | | | 16-00 (Associative rings and algebras :: General reference works ) | | | 20-00 (Group theory and generalizations :: General reference works ) |
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Pending Errata and Addenda
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