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Home > Art, Film & Photography > Ideals: Annihilator (Ring Theory), Associated Prime, Augmentation Ideal, Fractional Ideal, Going Up and Going Down, Ideal (Ord
Ideals: Annihilator (Ring Theory), Associated Prime, Augmentation Ideal, Fractional Ideal, Going Up and Going Down, Ideal (Ord

Ideals: Annihilator (Ring Theory), Associated Prime, Augmentation Ideal, Fractional Ideal, Going Up and Going Down, Ideal (Ord


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Annihilator (ring theory), Associated prime, Augmentation ideal, Fractional ideal, Going up and going down, Ideal (order theory), Ideal (ring theory), Ideal class group, Ideal norm, Ideal quotient, Ideal theory, Jacobian ideal, Jacobson radical, Krull's principal ideal theorem, Krull's theorem, Maximal ideal, Minimal ideal, Nilpotent ideal, Nilradical of a ring, Nil ideal, Primary ideal, Primitive ideal, Radical of an ideal, Regular ideal, Semiprime ring, Tight closure. Excerpt: In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any other integer results in another even number; these closure and absorption properties are the defining properties of an ideal. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may be distinct from the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ring. For instance, the prime ideals of a ring are analogous to prime numbers, and the Chinese remainder theorem can be generalized to ideals. There is a version of unique prime factorization for the ideals of a Dedekind domain (a type of ring important in number theory). An ideal can be used to construct a quotient ring similarly to the way that modular arithmetic can be defined from integer arithmetic, and also similarly to the way that, in group theory, a normal subgroup can be used to construct a quotient group. The concept of an order ideal...


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Product Details
  • ISBN-13: 9781230518404
  • Publisher: University-Press.Org
  • Publisher Imprint: University-Press.Org
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Weight: 68 gr
  • ISBN-10: 1230518401
  • Publisher Date: 12 Sep 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Annihilator (Ring Theory), Associated Prime, Augmentation Ideal, Fractional Ideal, Going Up and Going Down, Ideal (Ord
  • Width: 189 mm


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