Integral domain：16.4
16.4
Integral domain
https://en.wikipedia.org
In mathematics, specifically abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
代數導論二
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代數導論二- Integral Domain [TOC] ## 定義：Integral Domain :::warning 假定$R$ 是一個*ring*。若$R$ 滿足： ++*
Integral Domains
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A ring R is an integral domain if R = 0}, or equivalently. 1 = 0, and such that r is a zero divisor in R ⇐⇒ r = 0. Equivalently, a nonzero ring R is an ...
Integral Domain
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A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.
Section 19
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Every finite integral domain D is a field. Corollary (19.12). If p is a prime, then Zp is a field.
Definition
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An integral domain (D,+,∘) is a commutative ring such that (D∗,∘) is a monoid, all of whose elements are cancellable. In this context, D∗ ...
Mathematics
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A field is an integral domain. · A finite integral domain is a field. · A non trivial finite commutative ring containing no divisor of zero is an ...