principal ideal

principal ideal
the smallest ideal containing a given element in a ring; an ideal in a ring with a multiplicative identity, obtained by multiplying each element of the ring by one specified element.
[1935-40]

* * *


Universalium. 2010.

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  • 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

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  • 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

  • principal ideal — Math. the smallest ideal containing a given element in a ring; an ideal in a ring with a multiplicative identity, obtained by multiplying each element of the ring by one specified element. [1935 40] …   Useful english dictionary

  • principal ideal — noun An ideal which is generated by a single element of the ring …   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

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