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Prime ring

Let typeset structure be a commutative ring with identity typeset structure. If typeset structure is the ring of rational integers, then the map

λ : Z -> R,    λ(a) |-> a e(1)

is a ring-homomorphism. Its kernel is a principal ideal typeset structure, generated by an integer typeset structure.  The canonical injective (one-to-one) homomorphism typeset structure is a ring-homomorphism between typeset structure and a subring of typeset structure.

If in addition, typeset structure is an integral domain, then typeset structure is a prime ideal, and consequently either typeset structure or typeset structure for some prime number typeset structure.  

Cite this web-page as:

Štefan Porubský: Prime ring.

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