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Find a nonzero element in a ring that is neither a

Chapter 13, Problem 6E

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QUESTION:

Find a nonzero element in a ring that is neither a zero-divisor nor a unit.

Questions & Answers

QUESTION:

Find a nonzero element in a ring that is neither a zero-divisor nor a unit.

ANSWER:

Step 1 of 3

A ring  is a set with two binary operations, addition and multiplication, satisfying several properties:

 Is an Abelian group under addition, and the multiplication operation satisfies the associative law

                                                                             

And the distributive laws

                                                                             

And

                                                                             

For every

                                                                             

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