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See Also: prime element, irreducible, group of units, divisibility by prime number, gcd domain, corollary of Bézout's lemma, existence and uniqueness of the gcd of two integers, multiplication ring, ideal decomposition in Dedekind domain, ideal multiplication laws, unity plus nilpotent is unit, strict divisibility
| Also defines: |
divisible, divisibility, divisibility of ideals |
| Keywords: |
divide, divisor, factor |
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Cross-references: multiplication ring, ideal multiplication laws, ideals, ring, properties, semiring, unit, transitive relation, Reflexive, principal ideals, iff, zero divisors, non-zero unity, commutative ring
There are 145 references to this entry.
This is version 14 of divisibility in rings, born on 2004-10-08, modified 2007-03-19.
Object id is 6322, canonical name is DivisibilityInRings.
Accessed 5562 times total.
Classification:
| AMS MSC: | 11A51 (Number theory :: Elementary number theory :: Factorization; primality) | | | 13A05 (Commutative rings and algebras :: General commutative ring theory :: Divisibility) |
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Pending Errata and Addenda
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