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ideal-theoretic

См. также в других словарях:

  • Ideal (set theory) — In the mathematical field of set theory, an ideal is a collection of sets that are considered to be small or negligible . Every subset of an element of the ideal must also be in the ideal (this codifies the idea that an ideal is a notion of… …   Wikipedia

  • Ideal (order theory) — In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different… …   Wikipedia

  • theoretic — I (Roget s IV) modif. Syn. assumed, speculative, ideal; see theoretical . II (Roget s Thesaurus II) adjective 1. Existing only in concept and not in reality: abstract, hypothetic, hypothetical, ideal, theoretical, transcendent, transcendental.… …   English dictionary for students

  • Boolean prime ideal theorem — In mathematics, a prime ideal theorem guarantees the existence of certain types of subsets in a given abstract algebra. A common example is the Boolean prime ideal theorem, which states that ideals in a Boolean algebra can be extended to prime… …   Wikipedia

  • Algebraic number theory — In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number… …   Wikipedia

  • Twisted cubic — In mathematics, a twisted cubic is a smooth, rational curve C of degree three in projective 3 space mathbb{P}^3. It is a fundamental example of a skew curve. It is essentially unique, up to projective transformation ( the twisted cubic,… …   Wikipedia

  • Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   Wikipedia

  • Takagi existence theorem — In class field theory, the Takagi existence theorem states that for any number field K there is a one to one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K ) and the generalized… …   Wikipedia

  • Unique factorization domain — In mathematics, a unique factorization domain (UFD) is, roughly speaking, a commutative ring in which every element, with special exceptions, can be uniquely written as a product of prime elements, analogous to the fundamental theorem of… …   Wikipedia

  • Hilbert class field — In algebraic number theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K . Its degree over K equals the class number of K and the Galois group of E over K is canonically isomorphic to the ideal… …   Wikipedia

  • theoretical — I (New American Roget s College Thesaurus) adj. speculative, hypothetical, conjectural; unapplied; pure, abstract. See supposition. II (Roget s IV) modif. Syn. ideological, ideal, imaginative, unearthly, idealized, ideational, problematical,… …   English dictionary for students

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