prime subring

plural prime subrings

1. ring theoryalgebraThe image of the natural homomorphism from ℤ into R, which is the unique homomorphism mapping 1_ℤ to 1_R. Equivalently, the intersection of all subrings of R.

   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.

   2006, Shreeram Shankar Abhyankar, The Algebraic Structure of Crossed Products, World Scientific, page 21

   1 more example

   The image of the morphism f_A 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.

   2013, Michel Broué, Some Topics in Algebra: An Advanced Undergraduate Course at PKU, Springer Science & Business Media, page 10

   Synonyms: prime ring