In ring theory, a branch of mathematics, the zero ring or trivial ring is the unique ring (up to isomorphism) consisting of one element. (Less commonly, the term "zero ring" is used to refer to any rng of square zero, i.e., a rng in which xy = 0 for all x and y. This article refers to the one-element ring.)
Contents
In the category of rings, the zero ring is the terminal object, whereas the ring of integers Z is the initial object.
Definition
The zero ring, denoted {0} or simply 0, consists of the one-element set {0} with the operations + and · defined so that 0 + 0 = 0 and 0 · 0 = 0.
Properties
Constructions
References
Zero ring Wikipedia(Text) CC BY-SA