Q1)- Put true (T) or false (F) for thefollowing statements.Let K/L be ideal of quotientring R/L. If K is prime idealand contains L, then K/L isprime ideal.Let R be a commutative ringwith identity and I be ideal ofR. Then I is primary if andonly if every invertible in R/Iis a nilpotent.Let R be ring, then R isimbedded in the polynomialring R[X].The principal ideal (n) of thering Z is Maximal ideal, forany positive integer n.Let R be Boolean ring, If I isprime ideal of R ,then I ismaximal ideal of R.The set H={0,2,3}is a subringof (Z6, +6,.6) integer ringmodule 6.T FOO

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Answered: Let K/L be ideal of quotient ring R/L.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 13E

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17. Suppose is a ring with positive characteristic. Prove that if is any ideal of then is a multiple of the characteristic of.
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Since this section presents a method for constructing a field of quotients for an arbitrary integral domain D, we might ask what happens if D is already a field. As an example, consider the situation when D=5. a. With D=5, write out all the elements of S, sort these elements according to the relation , and then list all the distinct elements of Q. b. Exhibit an isomorphism from D to Q.
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Let K/L be ideal of quotient ring R/L. If K is prime ideal and contains L, then K/L is prime ideal. T F