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Algebra: Abstract and Modern by U. M. Swamy, A. V. S. N. Murthy

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10

Ideals and Quotient Rings

In the study of finite groups, we have proved several results using the concept of a normal subgroup, quotient construction and induction on the group order. Homomorphic images of groups are identified with quotient groups with the help of the kernel of the homomorphism which is a normal subgroup. The role of normal subgroups in groups is played by ideals in rings. The concepts of ideal and quotient rings are important in the structure theory of rings. A special kind of subrings, which are most suitable (ideal) for the study of the structure of rings, are popularly called ideals.

10.1 IDEALS ...

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