prime subring
English
editNoun
editprime subring (plural prime subrings)
- (algebra, ring theory, of a (unital) ring ) The image of the natural homomorphism from into , which is the unique homomorphism mapping to . Equivalently, the intersection of all subrings of .
- Synonym: prime ring
- 2006, Shreeram Shankar Abhyankar, The Algebraic Structure of Crossed Products, World Scientific, page 21:
- The image of the homomorphism ℤ→ R is called the prime subring of R. Clearly ch(R) = 0 ⟷ the prime subring of R is isomorphic to ℤ.
- 2013, Michel Broué, Some Topics in Algebra: An Advanced Undergraduate Course at PKU, Springer Science & Business Media, page 10:
- The image of the morphism fA is the prime subring of A. The prime subring is either isomorphic to the ring ℤ or isomorphic to the ring ℤ/nℤ for some n > 0.