Integral Domain
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Revision as of 19:49, 17 January 2023 by Kfagerstrom (talk | contribs) (Created page with "An 'Integral Domain', often just called domain, is a commutative ring <math>R </math>, with <math>1\neq 0 </math> and has no zero divisors. Any unital subring of an integral...")
An 'Integral Domain', often just called domain, is a commutative ring \(R \), with \(1\neq 0 \) and has no zero divisors.
Any unital subring of an integral domain is an integral domain.
An ideal is prime if and only if \(R/I \) is an integral domain.
Every field is an domain.
If \(R \) is a domain, \(S \) is a ring and \( f : R \to S\) is a ring homomorphism, then \(\text{Ker}(f)\) is a prime ideal.
