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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian
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In Z5[x], let . Find the multiplicative inverse of 2x + 3

Chapter 14, Problem 39E

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QUESTION:

In \(Z_5[x]\), let \(I=\left\langle x^2+x+2\right\rangle\). Find the multiplicative inverse of 2x + 3 +I in \(Z_5[x] / I\).

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QUESTION:

In \(Z_5[x]\), let \(I=\left\langle x^2+x+2\right\rangle\). Find the multiplicative inverse of 2x + 3 +I in \(Z_5[x] / I\).

ANSWER:

Step 1 of 4

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

         

And distributive laws

         

And

         

For every

          .

The identity of the addition operation is denoted 0. If the multiplication operation has an identity, it is called a 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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