25. Maximal Ideal - Definition and Questions

[@ramyakarthik239]

Respected sir, 1. Please Explain briefly about polynomial rings 2. How to find maximal ideal for the polynomial rings

[@samiransarkar3712]

Lagrange's theorem will only be applicable if the group is finite .

[@muhammadhanif460]

Thanks Sir💝💝...Well Explanation 👌👌👌👌

[@naeemshah5123]

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..

[@kalmabiyale3106]

Sir how every Ideal is a subgroup of ring

[@tesfawteshome3758]

It is nice to me. Please prove that every non zero ring has at least one maximal ideal.

[@AllyLearn]

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[@neelamsharma4502]

Thank you so much ☺️ 😍

[@goravgupta9334]

Marvellous explanation sir

[@AllyLearn]

For more lectures on Ring Theory and Higher Mathematics, download AllyLearn android app. Use invite code - NEW25 while registering and get 25 coins (limited period offer). Use these coins to unlock papers. Link play.google.com/store/apps/details?id=com.allylearn.app Regards, Team AllyLearn

[@zoniamalikzoniamalik]

an ideal in Z is maximal if and only if it is generated by a single prime number.why?Plz Answer this

[@Familysmile1235]

Thanks ☺

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[@AK-ij9rx]

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

[@AllyLearn]

Thanks for mentioning it we will look into it.

[@anabiyajawed3893]

How nz is equivalent to Zn?? Plzz clear it sr..

[@AllyLearn]

Please watch this lecture kzbin.info/www/bejne/mXKZqmicmKiMiq8. This will help you. Regards, Team AllyLearn

[@aparnaudayan6288]

Super class sir

[@SUJEETKUMAR-md5zr]

So nice sir Big fan of you sir

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[@saswatsir8552]

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

[@AllyLearn]

{0,3} will not form an ideal. Please, verify the definition of ideal. Hope this will help you. Regards, Team AllyLearn

[@aaryankaushal2017]

In the last question is contained in,then how can both and can be the maximal ideals of Z12

[@AllyLearn]

3 belongs to but 3 does not belong to so how can is contained in . Hope this will help you. Regards, Team AllyLearn

[@aaryankaushal2017]

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..???

[@AllyLearn]

@@aaryankaushal2017 yes... maximal ideals are not related to number of elements in the ideals.

[@vanshikasinghal4948]

In Z8, how come we didn't consider (5) & (6) &(7) when talking about ideal of order 2?

[@AllyLearn]

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

[@vanshikasinghal4948]

@@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?

[@bar_of_mathematics4]

@@vanshikasinghal4948 brother here we have to find maximal ideal so 4,5....both are considered but we have to find the maximal ideal

[@heisenbergmuzik4948]

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.

[@03_chiraggupta77]

Sir u have not properly explained the maximal ideal of Z4.😔

[@AllyLearn]

What this lecture - kzbin.info/www/bejne/h5e0iHqZnt9sirM You will be able to find maximal ideals of Zn. Regards, Team AllyLearn

[@ayushmantiwari7547]

Why have u put bar on elements of Z4 and Z8

[@AllyLearn]

Because they are equivalence classes.

[@nidhiraghav5419]

Sir apne videos private kyu krdi sir

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[@nidhiraghav5419]

@@AllyLearn ok

[@zoniamalikzoniamalik]

SuPerb💕...Thnx Al0t

[@AllyLearn]

Thanks for your valuable feedback.

[@ARTISHARMA-cb6lu]

Where is definition of ideal

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[@dhananjaysahani4470]

Nice sir

[@RideR-SAM65]

Thnku so much sir

[@sooraj137]

is only maximal ideal in Z12.how is maximal in this.

[@AllyLearn]

Try to solve it by yourself and just apply definition of Maximal Ideal.

[@saimasajid1540]

👍👍❤

[@شروقعامرطارشعلي]

find all a ideal inZ23

[@AllyLearn]

Please watch this lecture kzbin.info/www/bejne/h5e0iHqZnt9sirM. This will help you. Regards, Team AllyLearn

[@gunjansekhwal7177]

Sir smjh nhi aaya

[@AllyLearn]

Watch the lecture again you will get it, it's quite a simple concept.

[@zoniamalikzoniamalik]

an ideal in Z is maximal if and only if it is generated by a single prime number.why?Plz Answer this

[@AllyLearn]

You can prove it by definition of Maximal Ideal.

[@krishna-ojha-kakdwip]

Nice sir