Principal Ideal Domains

Some articles on principal ideal domains, principal ideal domain, domain, ideal, principal ideal:

Valuation Ring - Principal Ideal Domains
... A principal ideal domain, or PID, is an integral domain in which every ideal is a principal ideal ... A PID with only one non-zero maximal ideal is called a discrete valuation ring, or DVR, and every discrete valuation ring is a valuation ring ...

Famous quotes containing the words domains, principal and/or ideal:

    I shall be a benefactor if I conquer some realms from the night, if I report to the gazettes anything transpiring about us at that season worthy of their attention,—if I can show men that there is some beauty awake while they are asleep,—if I add to the domains of poetry.
    Henry David Thoreau (1817–1862)

    God should not be called an individual substance, since the principal of individuation is matter.
    Thomas Aquinas (c. 1225–1274)

    Realism absorbs the ideal by adding a few small imperfections. Example: it paints a few specks of mud on the white gown of the Lady in the Garden.
    Mason Cooley (b. 1927)