Algebraic number theory

Profinite integer

In mathematics, a profinite integer is an element of the ring (sometimes pronounced as zee-hat or zed-hat) where indicates the profinite completion of , the index runs over all prime numbers, and is the ring of p-adic integers. This group is important because of its relation to Galois theory, รฉtale homotopy theory, and the ring of adeles. In addition, it provides a basic tractable example of a profinite group. (Wikipedia).

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From playlist Introduction to Polynomials

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Galois theory | Restricted product | Chinese remainder theorem | Algebraic closure | Finite field | Frobenius endomorphism | Class field theory | Morphism of schemes | Algebraic torus | Supernatural number | Factorial number system | Hausdorff space | Direct product | ร‰tale homotopy type | ร‰tale fundamental group | Mathematics | Integer | Global field | Algebraic number theory | Ring (mathematics) | Absolute Galois group | Compact space | Prime number | Tychonoff's theorem | ร‰tale morphism | P-adic number | Profinite group | Commutative ring