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- (algebra, ring theory) Any nonzero commutative ring in which the product of nonzero elements is nonzero. [from 1911] 
- A ring is an integral domain if and only if the polynomial ring is an integral domain.
- For any integral domain there can be derived an associated field of fractions.
- 1990, Barbara H. Partee, Alice ter Meulen, Robert E. Wall, Mathematical Methods in Linguistics, Kluwer Academic Publishers, page 266,
- For integral domains, we will use a-1 to designate the multiplicative inverse of a (if it has one; since not all elements need have inverses, this notation can be used only where it can be shown that an inverse exists).
- 2013, Marco Fontana, Evan Houston, Thomas Lucas, Factoring Ideals in Integral Domains, Springer, page 95,
- An integral domain is said to have strong pseudo-Dedekind factorization if each proper ideal can be factored as the product of an invertible ideal (possibly equal to the ring) and a finite product of pairwise comaximal prime ideals with at least one prime in the product.
- 2017, Ken Levasseur, Al Doerr, Applied Discrete Structures: Part 2 - Applied Algebra, Lulu.com, page 171,
- , with a prime, , , and are all integral domains. The key example of an infinite integral domain is . In fact, it is from that the term integral domain is derived. Our main example of a finite integral domain is , when is prime.
- (commutative ring in which the product of nonzero elements is nonzero): entire ring
nonzero commutative ring in which the product of nonzero elements is nonzero