In mathematics, especially in the area of algebra known as ring theory, a semiprimitive ring is a type of ring more general than a semisimple ring, but where simple modules still provide enough information about the ring. Important rings such as the ring of integers are semiprimitive, and an artinian semiprimitive ring is just a semisimple ring. Semiprimitive rings can be understood as subdirect products of primitive rings, which are described by the Jacobson density theorem. The quotient of every ring by its Jacobson radical is semiprimitive, allowing every ring to be understood to some extent through semiprimitive rings.
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Famous quotes containing the word ring:
“Generally, about all perception, we can say that a sense is what has the power of receiving into itself the sensible forms of things without the matter, in the way in which a piece of wax takes on the impress of a signet ring without the iron or gold.”
—Aristotle (384–323 B.C.)