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Math / Contemporary Abstract Algebra 8 / Chapter 14 / Problem 19E

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

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Give an example of a ring that has exactly two maximal

Chapter 14, Problem 19E

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QUESTION:

Give an example of a ring that has exactly two maximal ideals.

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QUESTION:

Give an example of a ring that has exactly two maximal ideals.

ANSWER:

Step 1 of 5

A ring R is a set with two binary operations, additions and multiplication, satisfying several properties: R is an Abelian group under addition, and the multiplication, and the operation satisfies the associative law

And distributive laws

For every

The identity of the addition operation is denoted 0. If the multiplication operation has an identity. It is called unity. If multiplication is commutative, we say that R is commutative.

A subring of a ring R is a subset

That is a ring under the operations of R.

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