### Some articles on *prime, gaussian primes, gaussian*:

Prime Number - Generalizations - Prime Elements in Rings

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**Prime**numbers give rise to two more general concepts that apply to elements of any commutative ring R, an algebraic structure where addition, subtraction and multiplication are ... An element p of R is called**prime**element if it is neither zero nor a unit (i.e ... In the ring Z of integers, the set of**prime**elements equals the set of irreducible elements, which is In any ring R, any**prime**element is irreducible ...List Of Prime Numbers - Lists of Primes By Type -

... Prime elements of the Gaussian integers (primes of form 4n + 3). ...

**Gaussian Primes**... Prime elements of the Gaussian integers (primes of form 4n + 3). ...

Gaussian Integer - As A Principal Ideal Domain

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**Gaussian**integers form a principal ideal domain with units 1, −1, i, and −i ... If x is a**Gaussian**integer, the four numbers x, ix, −x, and −ix are called the associates of x ... As for every principal ideal domain, the**Gaussian**integers form also a unique factorization domain ...