Discrete Mathematical Structures by Pearson

Algebraic Structures 7-43

It can be shown that the set R[x] of all polynomials over a ring R in symbol x with coefficients

in ring R is a ring under polynomial addition and multiplication.

7.11.4 Morphism of Rings

A mapping f from a ring R to a ring S is called a morphism if

f(ab) = f(a) f(b) ∀a,b ∈ R

A mapping f from a ring R to a ring S is called a homomorphism if

f (a+b) = f(a) + f(b), and f(ab) = f(a) f(b) for ever a,b ∈ R

Monomorphism: A homomorphism f: R → S is called monomorphism if f is one-to-one and

epimorphism if f is ONTO.

Isomorphism: A homomorphism f:R → S is called isomorphism if f is both one to one

and onto.

Endomorphism: A homomorphism f: R → R, that is, ring R into R itself, is called endomorphism.

Automorphism: An isomorphism ...