Ring Homomorphism
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication.A bijective ring homomorphism is called a ring isomorphism. A ring homomorphism whose domain is the same as its range is called a ring endomorphism. A ring automorphism is a bijective endomorphism.Injective ring homomorphisms are identical to monomorphisms in the category of rings: If f:R S is a monomorphism which is not ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication.A bijective ring homomorphism is called a ring isomorphism. A ring homomorphism whose domain is the same as its range is called a ring endomorphism. A ring automorphism is a bijective endomorphism.Injective ring homomorphisms are identical to monomorphisms in the category of rings: If f:R S is a monomorphism which is not injective, then it sends some r1 and r2 to the same element of S. Consider the two maps g1 and g2 from Z[x] to R which map x to r1 and r2, respectively; f o g1 and f o g2 are identical, but since f is a monomorphism this is impossible.
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