product of left and right ideal

Let π”ž and π”Ÿ be ideals of a ring R.  Denote by  π”žβ’π”Ÿβ€‰ the subset of R formed by all finite sums of productsPlanetmathPlanetmath a⁒b with  aβˆˆπ”žβ€‰ and  bβˆˆπ”Ÿ.  It is straightforward to verify the following facts:

  • β€’

    If π”ž is a left ( and π”Ÿ a right idealMathworldPlanetmath, π”žβ’π”Ÿβ€‰ is a two-sided ideal of R.

  • β€’

    If both π”ž and π”Ÿ are two-sided ideals, then  π”žβ’π”ŸβŠ†π”žβˆ©π”Ÿ.

Title product of left and right ideal
Canonical name ProductOfLeftAndRightIdeal
Date of creation 2013-03-22 17:38:09
Last modified on 2013-03-22 17:38:09
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Theorem
Classification msc 16D25
Related topic ProductOfIdeals
Related topic IntersectionMathworldPlanetmath
Related topic IdealMultiplicationLaws