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Show that 0 is the only nilpotent element in an integral

Chapter 13, Problem 17E

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QUESTION:

Problem 17E

Show that 0 is the only nilpotent element in an integral domain.

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QUESTION:

Problem 17E

Show that 0 is the only nilpotent element in an integral domain.

ANSWER:

Step 1 of 4

A ring R is a set with two binary operations such as addition and multiplication that satisfies several properties.

R is an Abelian group under addition and multiplication operation satisfies the associative law.

                                                               

According to distributive laws

                                                       

For every

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