prime subring
prime subring noun: the 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.
Noun
prime subring (plural prime subrings)
- The 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
- 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
Synonyms of prime subring
Forms of prime subring
| plural | prime subrings |
|---|
Questions about prime subring
- What does prime subring mean?
- Prime subring means the 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.
- What part of speech is prime subring?
- Prime subring is a noun.
- What is the plural of prime subring?
- The plural of prime subring is prime subrings.
Words near prime subring in the dictionary
Source and license
Adapted from Wiktionary: prime subring (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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