Number 25 24. Show that a factor ring of a field is either the trivial (zero) ring of one element or is isomorphic to the field.25. Show that if R is a ring with unity and N is an ideal of R such that N R, then R/N is a ring with unity.

Name: Number 25 24. Show that a factor ring of a field is either the trivial
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Description: Number 25 24. Show that a factor ring of a field is either the trivial (zero) ring of one element or is isomorphic to the field.25. Show that if R is a ring with unity and N is an ideal of R such that N R, then R/N is a ring with unity.

Since we have given that R is a ring with unity and N is a proper ideal of R . We prove R/N is a…

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Show that if R is a ring with unity and N is an ideal of R such that N R, then R/N is a ring with unity.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .

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The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

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Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

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The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

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Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

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Number 25

24. Show that a factor ring of a field is either the trivial (zero) ring of one element or is isomorphic to the field.
25. Show that if R is a ring with unity and N is an ideal of R such that N R, then R/N is a ring with unity.

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