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In Z8 if we consider principal ideal generated by 3 that is we get {0,1,2,3,4,5,6,7} All numbers in Z8 But in the video it is mentioned that ={0,3,6} only
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Thanks... You can now watch our latest lectures on our android app. The benefits of our app are: 1. It is FREE 2. No annoying ad 3. Save upto 80% data with highly optimized videos. 4. Syllabus, notes and topic wise lectures are available. The link of the app is here play.google.com/store/apps/details?id=com.allylearn.app Regards, Team AllyLearn
me jese 3 ke multiple leke test kiye, 1st example me bhi to 3 k multiple le sakte he. Agar 1st example me 3 k multiple lenge to aur ek ideal aa sakta he {0,3} aur iska order bhi 2 he, upar se 2|4. Please explain sir
Misleading!!! You have used converse of Lagrange theorem. So, you must have mentioned it is abelian group coz Lagrange converse is true for abelian groups only. Rather you should have stated following theorem- order of subgroup of every cyclic group is factor of the order of group. Here, Z4 is cyclic.
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So can we conclude that it is not necessary that maximal ideal should have maximum number of elements becausehas more elements than but both are maximal ideals..???
By Lagrange theorem order of subgroup divides order of Group. Therefore, we are considering only those sets/subgroup whose number of elements divides order of G. Hope, this will help you. Regards, Team AllyLearn
@@AllyLearn Sir suppose we look in Z12. In this we have to find an ideal of order 3. Both {0, 4,8} and {0, 5,10} satisfy the conditions of ideal. Then which will we consider?
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Respected sir,
1. Please Explain briefly about polynomial rings
2. How to find maximal ideal for the polynomial rings
It is nice to me. Please prove that every non zero ring has at least one maximal ideal.
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Lagrange's theorem will only be applicable if the group is finite .
Let I be an ideal of ring R. Then I is maximal iff (I, a) = R where (I, a) = I + .. Please make a video on this..
Thanks Sir💝💝...Well Explanation 👌👌👌👌
Thanks ☺
अगले पांच मिनट आपके Maths पढ़ने का तरीका बदल सकते हैl
Download the Allylearn app now and start learning from 900+ video lectures and Notes
No registration required for a try
पहले इस्तेमाल करें फिर विश्वाश करें l
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Hope you like our work
Regards,
Team AllyLearn
In Z8 if we consider principal ideal generated by 3 that is
we get
{0,1,2,3,4,5,6,7}
All numbers in Z8
But in the video it is mentioned that
={0,3,6} only
Thanks for mentioning it we will look into it.
Marvellous explanation sir
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Sir how every Ideal is a subgroup of ring
Super class sir
Thank you so much ☺️ 😍
So nice sir
Big fan of you sir
Thanks...
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1. It is FREE
2. No annoying ad
3. Save upto 80% data with highly optimized videos.
4. Syllabus, notes and topic wise lectures are available.
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Regards,
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an ideal in Z is maximal if and only if it is generated by a single prime number.why?Plz Answer this
me jese 3 ke multiple leke test kiye, 1st example me bhi to 3 k multiple le sakte he.
Agar 1st example me 3 k multiple lenge to aur ek ideal aa sakta he {0,3} aur iska order bhi 2 he, upar se 2|4.
Please explain sir
{0,3} will not form an ideal. Please, verify the definition of ideal. Hope this will help you.
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Team AllyLearn
Misleading!!! You have used converse of Lagrange theorem. So, you must have mentioned it is abelian group coz Lagrange converse is true for abelian groups only. Rather you should have stated following theorem- order of subgroup of every cyclic group is factor of the order of group. Here, Z4 is cyclic.
Thnku so much sir
Sir u have not properly explained the maximal ideal of Z4.😔
What this lecture - th-cam.com/video/QfQWGciz9TQ/w-d-xo.html
You will be able to find maximal ideals of Zn.
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Team AllyLearn
SuPerb💕...Thnx Al0t
Thanks for your valuable feedback.
Sir apne videos private kyu krdi sir
Taki aap log humari app par aur ache se padh sake.
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@@AllyLearn ok
In the last question
is contained in,then how can both and can be the maximal ideals of Z12
3 belongs to but 3 does not belong to so how can is contained in .
Hope this will help you.
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Team AllyLearn
So can we conclude that it is not necessary that maximal ideal should have maximum number of elements becausehas more elements than but both are maximal ideals..???
@@aaryankaushal2017 yes... maximal ideals are not related to number of elements in the ideals.
Nice sir
In Z8, how come we didn't consider (5) & (6) &(7) when talking about ideal of order 2?
By Lagrange theorem order of subgroup divides order of Group. Therefore, we are considering only those sets/subgroup whose number of elements divides order of G.
Hope, this will help you.
Regards,
Team AllyLearn
@@AllyLearn Sir suppose we look in Z12. In this we have to find an ideal of order 3. Both {0, 4,8} and {0, 5,10} satisfy the conditions of ideal. Then which will we consider?
@@vanshikasinghal4948 brother here we have to find maximal ideal so 4,5....both are considered but we have to find the maximal ideal
Why have u put bar on elements of Z4 and Z8
Because they are equivalence classes.
Where is definition of ideal
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find all a ideal inZ23
Please watch this lecture th-cam.com/video/QfQWGciz9TQ/w-d-xo.html. This will help you.
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Team AllyLearn
👍👍❤
Sir smjh nhi aaya
Watch the lecture again you will get it, it's quite a simple concept.
is only maximal ideal in Z12.how is maximal in this.
Try to solve it by yourself and just apply definition of Maximal Ideal.
Nice sir
an ideal in Z is maximal if and only if it is generated by a single prime number.why?Plz Answer this
You can prove it by definition of Maximal Ideal.