Back Dominio (álgebra) Spanish Anneau sans diviseur de zéro French 非可換整域 Japanese 영역 (환론) Korean Domínio (teoria dos anéis) Portuguese Domeniu (teoria inelelor) Romanian Domena (teorija kolobarjev) Slovenian Domän (ringteori) Swedish
In algebra, a domain is a nonzero ring in which ab = 0 implies a = 0 or b = 0.[1] (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A commutative domain is called an integral domain.[1][2] Mathematical literature contains multiple variants of the definition of "domain".[3]
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- ^ a b Lam (2001), p. 3
- ^ Rowen (1994), p. 99.
- ^ Some authors also consider the zero ring to be a domain: see Polcino M. & Sehgal (2002), p. 65. Some authors apply the term "domain" also to rngs with the zero-product property; such authors consider nZ to be a domain for each positive integer n: see Lanski (2005), p. 343. But integral domains are always required to be nonzero and to have a 1.