In mathematics, a left primitive ideal in ring theory is the annihilator of a simple left module. A right primitive ideal is defined similarly. Note that (despite the name) left and right primitive ideals are always two-sided ideals.
The quotient of a ring by a left primitive ideal is a left primitive ring.
Famous quotes containing the words primitive and/or ideal:
“It was a very primitive kind of harbor, where boats were drawn up amid the stumps,—such a one, methought, as the Argo might have been launched in.”
—Henry David Thoreau (1817–1862)
“Every epoch which seeks renewal first projects its ideal into a human form. In order to comprehend its own essence tangibly, the spirit of the time chooses a human being as its prototype and raising this single individual, often one upon whom it has chanced to come, far beyond his measure, the spirit enthuses itself for its own enthusiasm.”
—Stefan Zweig (18811942)