Zero ring | StudentB Wikipedia Search

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In ring theory, a branch of mathematics, the zero ring^[1]^[2]^[3]^[4]^[5] 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.)

In the category of rings, the zero ring is the terminal object, whereas the ring of integers Z is the initial object.

^ Artin 1991, p. 347
^ Atiyah & Macdonald 1969, p. 1
^ Bosch 2012, p. 10
^ Bourbaki, p. 101
^ Lam 2003, p. 1