Define integral domain.
Understand the Problem
The question is asking for the mathematical definition of an integral domain, which is a specific type of algebraic structure in abstract algebra, particularly in ring theory. An integral domain is a commutative ring with no zero divisors and where 1 is not equal to 0. We will explain this concept clearly and concisely.
Answer
A nonzero commutative ring with no zero divisors.
An integral domain is a nonzero commutative ring with no zero divisors.
Answer for screen readers
An integral domain is a nonzero commutative ring with no zero divisors.
More Information
In an integral domain, if the product of two elements is zero, then at least one of the elements must be zero.
Tips
A common mistake is neglecting to verify that a ring is commutative when identifying an integral domain.
Sources
- Integral domain - Wikipedia - en.wikipedia.org
- 16.4: Integral Domains and Fields - Mathematics LibreTexts - math.libretexts.org
- Integral Domains - Department of Mathematics at UTSA - mathresearch.utsa.edu
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