Reference no: EM131027839
Note: Z is integer numbers
C is set containment
Here is the problem
Let I be an ideal in a ring R.
Define [ R : I ] = { r in R such that xr in R for all x in R }
1) Show that [ R : I ] is an ideal of R that contains I
2) If R is assumed to have a unity, what can you say about [ R : I ] ?
3) Find [ 2Z : 12Z ], where 2Z is the ring of even integers
For part 1) Please, pay careful attention to all the property you must verify to show that something is an ideal in a ring that is not assumed to be commutative.
For example,
i) closure under addition
ii) 0 in [ R : I ]
iii) If r in [ R : I ], then -r (inverse of r) in [ R : I ]
iv) aN C N, and Nb C N where a, b in R and N is additive subgroup of a ring R
Thousands of stockholders lost millions
: After the scandal was uncovered, thousands of stockholders lost millions of dollars as Enron share values plummeted."
|
Determine the probability distribution for y
: Consider a system of water flowing through valves from A to B. (See the accompanying diagram.) Valves 1, 2, and 3 operate independently, and each correctly opens on signal with probability .8. Find the probability distribution for Y , the number o..
|
Prove that if is a ring homomorphism
: Write down two distinct maximal ideals of . Does have a finite or infinite number of maximal ideals? Give brief reasons for your answer.
|
What percentage increase is forecast for the next six month
: What is the Dow Forecast to be in six months? What percentage increase is forecast for the next six month? Using the method presented here in this chapter, move the data into an excel spreadsheet.
|
What can you say about [ r : i ]
: Please, pay careful attention to all the property you must verify to show that something is an ideal in a ring that is not assumed to be commutative.
|
Appropriate for determining eoq
: Brodie is uncertain if the costs presented in case Exhibit 2 are appropriate for determining EOQs. What changes would you recommend and why? Should the cost of the three idle part-time workers be included when the production line is down?
|
Find the probability distribution for y
: An inspector tests the components one at a time until the two defectives are located. Once she locates the two defectives, she stops testing, but the second defective is tested to ensure accuracy. Let Y denote the number of the test on which the s..
|
What is important and meaningful in folk art
: What is important and meaningful in folk art? **Consider personal and cultural meaning. Consider the values and traditions of other people represented by the art object. Address one's ability to make critical judgments about folk art, free from n..
|
Find probability distribution for y number of impurities
: When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 20% of the wells had neither impurity, 40% had impurity A, and 50% had impurity B. (Obviously, some had both impurities...
|