An integral element is a term used in various fields, primarily in mathematics and abstract algebra, as well as in related contexts like computer science and physics. However, without a specific context, the meaning can vary. 1. **Mathematics/Abstract Algebra**: In ring theory, an integral element refers to an element of an integral domain (a type of commutative ring) that satisfies a monic polynomial equation with coefficients from that domain.
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An element of an -algebra is integral over when it satisfies a monic polynomial with coefficients in .