symmetric monoidal (∞,1)-category of spectra
Given a unital (typically noncommutative) ring , the Jacobson radical is defined as the set of elements satisfying the following equivalent properties:
Alternatively,
The properties required remain the same if one interchanges left and right (modules, invertibility etc.) i.e. .
is a -sided ideal in . The rings for which are called semiprimitive rings. In other words, for each nonzero element in a semiprimitive ring, by the definition, there is a simple module not left annihilated by . Given any ring , the quotient is semiprimitive.
(Jacobson radical of formal power series algebra)
The Jacobson radical of a formal power series algebra consists of those formal power series whose constant term vanishes.
See also
Last revised on June 1, 2021 at 23:29:11. See the history of this page for a list of all contributions to it.