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zero ring
In ring theory, a branch of mathematics, the zero ring〔Artin, p. 347.〕〔Atiyah and Macdonald, p. 1.〕〔Bosch, p. 10.〕〔Bourbaki, p. 101.〕〔Lam, p. 1.〕 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 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.
==Definition==
The zero ring, denoted or simply 0, consists of the one-element set with the operations + and · defined so that 0 + 0 = 0 and 0 · 0 = 0.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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