Maximal Ideals in Commutative Rings: Explained and Solved

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A proper ideal I of a commutative ring R is a maximal ideal if and only if for any ideal A of R, either A is a subset of I or the sum A + I equals R. The discussion emphasizes understanding the definition of a maximal ideal as a crucial starting point for solving related problems. Participants express confusion about why textbook problems can be challenging, indicating that familiarity with definitions and concepts is essential. Clarifying the properties of maximal ideals can aid in grasping their significance in ring theory. Mastery of these concepts is necessary for tackling complex problems in commutative algebra.
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hi , pleasehelp me

itry to soution this question but ican not , because this out my book


Show that a proper ideal I of a commmutative ring R is a maximal ideal iff for any ideal A of R either A subset of I or A+I=R
 
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Why would you not be able to get a solution just because this is from the book?
 
Start with the definition: What is the definition of "maximal ideal"?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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