prime ring
In algebra, a "prime ring" is crucial for understanding the structure and properties of rings, particularly in ring theory.
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Definition
C2Ring Theory
(technical, academic)A non-zero ring where the product of any two non-zero ideals is non-zero.
Example
- In a prime ring, the interaction between ideals follows strict rules that prevent the product from being zero unless one of the ideals is zero.
- Studying prime rings helps in understanding more complex algebraic structures.
Similar
Terms that have similar or relatively close meanings to "prime ring":
local ringprincipal ideal ringring offring inring timeiron ringring gamediamond ringordered ringhold the ringprime ideal