### Some articles on *ideal, primary, primary ideal, primary ideals, ideals*:

Primary Ideal

... In mathematics, specifically commutative algebra, a proper

... In mathematics, specifically commutative algebra, a proper

**ideal**Q of a commutative ring A is said to be**primary**if whenever xy is an element of Q then x or yn is also an element of Q, for some n>0 ... For example, in the ring of integers Z, (pn) is a**primary ideal**if p is a prime number ... The notion of**primary ideals**is important in commutative ring theory because every**ideal**of a Noetherian ring has a**primary**decomposition, that is, can be written as an intersection of finitely ...Lasker–Noether Theorem - Irreducible Decomposition in Rings

... The study of the decomposition of

... The study of the decomposition of

**ideals**in rings began as a remedy for the lack of unique factorization in number fields like , in which ... If a number does not factor uniquely into primes, then the**ideal**generated by the number may still factor into the intersection of powers of prime**ideals**... Failing that, an**ideal**may at least factor into the intersection of**primary ideals**...Noetherian Ring - Primary Decomposition

... In the ring of integers, an arbitrary

... In the ring of integers, an arbitrary

**ideal**is of the form (n) for some integer n (where (n) denotes the set of all integer multiples of n) ... In this case, the**ideal**(n) may be written as the intersection of the**ideals**(piei) that is ... This is referred to as a**primary**decomposition of the**ideal**(n) ...### Famous quotes containing the words ideals and/or primary:

“You can tell the *ideals* of a nation by its advertisements.”

—Norman Douglas (1868–1952)

“The *primary* imperative for women who intend to assume a meaningful and decisive role in today’s social change is to begin to perceive themselves as having an identity and personal integrity that has as strong a claim for being preserved intact as that of any other individual or group.”

—Margaret Adams (b. 1916)

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