principal ideal domain

主理想域

English-Chinese computer dictionary (英汉计算机词汇大词典). 2013.

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  • Principal ideal domain — In abstract algebra, a principal ideal domain, or PID is an integral domain in which every ideal is principal, i.e., can be generated by a single element.Principal ideal domains are thus mathematical objects which behave somewhat like the… …   Wikipedia

  • principal ideal domain — Math. a commutative integral domain with multiplicative identity in which every ideal is principal. Also called principal ideal ring. [1960 65] * * * …   Universalium

  • principal ideal domain — Math. a commutative integral domain with multiplicative identity in which every ideal is principal. Also called principal ideal ring. [1960 65] …   Useful english dictionary

  • principal ideal domain — noun An integral domain in which every ideal is a principal ideal …   Wiktionary

  • Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… …   Wikipedia

  • Principal ideal — In ring theory, a branch of abstract algebra, a principal ideal is an ideal I in a ring R that is generated by a single element a of R .More specifically: * a left principal ideal of R is a subset of R of the form R a := { r a : r in R }; * a… …   Wikipedia

  • Principal ideal ring — In mathematics, a principal ideal ring, or simply principal ring, is a ring R such that every ideal I of R is a principal ideal, i.e. generated by a single element a of R .A principal ideal ring which is also an integral domain is said to be a… …   Wikipedia

  • Domain — may refer to: General Territory (administrative division), a non sovereign geographic area which has come under the authority of another government Public domain, a body of works and knowledge without proprietary interest Eminent domain, the… …   Wikipedia

  • Ideal class group — In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by a certain group known as an ideal class group (or class group). If… …   Wikipedia

  • Ideal (ring theory) — In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like even number or multiple of 3 . For instance, in… …   Wikipedia

  • Ideal norm — In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an… …   Wikipedia

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