Ring Theory | Integral Domain | Integral Domain Examples | Theorems / Definitions

[@gajendrapurohit]

Thanks for your comment, your appreciation always motivate us to do such kind work. Join Telegram Channel : t.me/mathsbygpsir Instagram Handle : instagram.com/dr.gajendrapurohit/ Facebook Page : facebook.com/Dr-Gajendra-Purohit-453775988491992/ Unacademy : unacademy.com/@Dr-GajendraPurohit Link to B.Sc. Maths Playlist : bit.ly/34tTTdc Link to Engineering Maths Playlist : bit.ly/2OQ7Uvd Link to IIT-JAM Maths Playlist : bit.ly/2sh9pei Link to GATE (Engg.) Maths Playlist : bit.ly/35EAPct Link to IAS Optional Maths Playlist : bit.ly/2rwkOqj Link to CSIR NET Maths Playlist : bit.ly/2R8sUjV Link to Aptitude Playlist : bit.ly/3ewDR7z Link to Mathematical Physics Playlist : bit.ly/2NvRHLJ Link to Abstract Algebra Playlist : bit.ly/2A70LUb Link to General Aptitude For CSIR NET : bit.ly/2ZeWpma Follwing Topics are also Available 1. Differential Calculus : bit.ly/2OTYXB0 2. Integral Calculus : bit.ly/34rLA1R 3. Differential Equation : bit.ly/37IOlO1 4. Partial Differential Equation : bit.ly/2OM5iyA 5. Complex Analysis : bit.ly/2OP8hGp 6. Numerical Analysis : bit.ly/2QYVQuy 7. Integral Transform (Laplace, Fourier & Z-Transform) : bit.ly/37HRKg9 8. Statistics & Probability : bit.ly/2DmOt7Z 9. Operation Research : bit.ly/2pYYRjp 10. Matrices (Linear Algebra) : bit.ly/2OOBSzO 11. Fourier Series : bit.ly/34u7iC9 12. Vector Calculus : bit.ly/2qICwXO 13. Theory Of Equation : bit.ly/2XU9y33 14. Special Function & Series Solution : bit.ly/2XRSU4l 15. Infinite Series : bit.ly/37K6gUI 16. Group Theory : bit.ly/3ieUze2 Please share it with your Friends Thanks Dr.Gajendra Purohit

[@upsctarget3012]

tq sir

[@AbhishekVerma-cm4go]

Sir mechanics ka material nahi available hai kya?

[@amazingfact2921]

Sir you are the best 🙏

[@Krishna-zk9iz]

Arts ka student bhi apse maths pdhkr top kr skta h sir Seriously life me mujhe itna achha tutor maths ka nhi mila ✨👏👏 thnkyou so much sir 👑

[@amanbhati4719]

For all those confused about theoram here is my understanding of this matter. Let 'p' be not a prime number. Which means that 'p = p1 multiple p2' And ( p1 and p2 are elements of Zp ). Now [ p1 multiply_modulo(p) p2 = 0 ] Because p1 and p2 both are not equal to 0 that means that Zp is with zero divisor And it contradict the idea of Zp being integral domain. So it means tha p must be a prime in order to Zp being a integral domain.

[@samridhisingh19]

@Aman Bhati Thank you 👍🏻

[@gauravpant6651]

P is prime. a (multi_mod_p) b =0 and p divides ab, Then how can we say that a=0 or b=0...?????????? They both may be zero..

[@vgouravdancext2704]

​@@gauravpant6651Bro The Multiply Modulo Must Be Different From A And B... 😂😂

[@Dusk425]

Thank you so much sir I have already completed my bsc but my knowledge in group theory used to be very poor. Your videos have been really useful. Through your videos I hope to fully understand group theory.

[@rajarammishra255]

Ghar baithe padhai ho rhi hai sir aap ki wajah se. Thanks a lot sir.

[@manoharsain434]

3d ke video uploade kro sir ji Aap both acha samjate ho Thanks sir 🙏👍

[@fyadmohammed8856]

So much interactive and awesome lectures sir. Thank you so much .

[@beautifulstatus8369]

Sir apke explaination bahut acha h sunkr concept clr ho gya mera

[@monuchouhan4333]

only say this for u sirji u r bestest teacher of maths🙏🙏🙏🙏🙏🙂🙂

[@ashishshukla7144]

Sir after complete this helpful topic. Please upload videos on vector space. Thank you so much for this sympathy. 🙏🙏👍👍

[@sujoypaul1874]

after 3 years of failing in applied mathematics i can now finally pass exams because of you.Thank you sir,you are a life saver

[@Haseeb-if4yx]

Is the ring theory applied mathematics

[@zariialezy952]

@@Haseeb-if4yx pure.

[@ankitkumardip90]

@@Haseeb-if4yx ring theory is pure mathematics

[@ankitkumardip90]

This is pure mathematics bro

[@namrashabbir6873]

IC lye Tu bichara fail huta rha😂

[@bhanubatra8543]

Sir aapne humare semester bacha lie ...thanku 💫🥰

[@vinitaa3494]

Sir teaching speed and skills are very good.. it's very helpful to all students. Sir please upload the video about vector space and linear transformation.

[@shivanigupta13]

Sir ur explanation is great....it helps me a lot... thank u so much ❤️

[@radheshyam-oo8hg]

Howww are yu frnd shivi

[@mustafaahmed920]

Sir,your explanation contains detailed information and is luicid.Thank you very much sir 👍👍👍......please upload the remaining topics...

[@tanyasanjay9711]

Thank you for this sir .. I left this part in coaching 🙏🏻

[@eldhaelizabeth4856]

It's amazing class.. can you do it English or can you add subtitles..

[@Rankrank-r3b]

Thanks sir for everything you do selflessly 🙌

[@beinghuman7446]

Sir Real analysis ke opar video kab aayega?

[@shyamsundarmariya8801]

Great teacher, Love you sir

[@sitabalai8736]

At 2:42 I think it is multiplicative modulo which is equal to zero and not the product of two numbers . Correct me if I am wrong.

[@PraveenKumar-ps2tn]

No it is product not modulo

[@NeerajVerma-nb1ww]

Sir you are the best teacher

[@muhammadsaqibulhassan8400]

Sir u r great .....u r lectures are sooo helpful for me .....

[@divijpandey5439]

Thanks sir..🙏🏻🙏🏻🙏🏻♥️ very helpful

[@rahulnamanverma4445]

JAI GORISHANKAR JI JAI SIYARAM JI

[@rahulnamanverma4445]

JAI RADHESHYAM JI JAI HANUMAN JI

[@souravbhagat9979]

sir please make a video on Normal form DNf and cnf . And permutation and combinations

[@abhinandanjain2399]

Thank you so much sir 🙏 🙏🙏🙏🙏🙏 nice video.

[@anmolrana2503]

Sir Can you Recommend me a book for farther Studies , I am from CS and i am studying these under Discreet Structures .

[@TulasiNishad-jt6lv]

Thank you so much sir 🙏🙏🙏❤❤❤for your hard work for us😊😊😊.

[@msuresh2756]

Super sir thank you Many doubts clear about integral domail

[@nabeelkhalid3727]

ID need not to have unity in it.... Only commutative ring with no zero divisor is complete definition. I dont know y u are taking unity as condition can u explain?

[@tanunamdev9775]

Sir vector book ke chapter per video dalo sir plzzzzz

[@gaanagaana527]

Sir apne bataya ki composite number ha to multiplication of two prime numbers hoga, 8 ek composite number ha and 8=4x2 , 2 is prime but 4 to prime nahi hai!! ????

[@surajb127]

Thank you sir, ap a66i samjhate ho. ❤

[@UmeshKumar-jr4dm]

Best teacher the app

[@zunnurainzunnurain7085]

Great work sir .

[@tusharboda754]

Sir you said that you will upload video on 'books for iit jam maths' sir pls make a video on this.

[@mehsaransari6113]

thank you sir for the wonderfull lecture

[@mehakbansal9701]

Sir pls complete lectures of ring

[@Rp63888]

Nice class sir 🙏🙏🙏🙏

[@mahararshad3503]

Love you sir on you efforts, from Pakistan 🇵🇰, Carry-on, God bless you with more abilities, wisdom 💞

[@garimaasopa8019]

Sir please upload video on Dynamics

[@khemrajchaulagai6855]

sir please make the video of field.

[@SukhwinderSingh-iq3cc]

Sir mujhe LINER ALGEBRA -|| Ki tution ki jroort ha Jikar ap aur kyoi bhi mujhe deye ta plz bta sir Mujhe bhut jroort hai 🙏🏻

[@amankumarrollno1777]

Sir congruence of triangle par video

[@amityadav-gs4xx]

Sir plz discuss some ob.. Problem depends upon every topics

[@ADARSHKUMAR-qo9ye]

Bahut achaa sir

[@beinghuman7446]

Thank u sir....sir abstract algebra ka koi book suggest karona plz

[@DevendraKumar-kh8li]

Thanks sir 👍🏿👍🏿

[@aimers3571]

Hello sir ,app IAS mains ke mathematics ka syllabus bhi padhye

[@nikitayadav8949]

Thanku sir for valuable lecture

[@netralalpariyar3507]

Best for learning

[@PCShindiwala]

Sir ideal pr class le lijie please

[@sagarchacherkar5319]

Thank you so much 💐.........sir

[@kv-gw6bf]

Only definition of integral fx = sin< 1/x> x irrational 0 otherwise 0

[@pritishalini202]

Sir.... any example of simple Abelian ring R which is not domain? 🤔 Is Z6 is right answer or not

[@madhubarnwal..]

Ha

[@AjayKumar-kx5fi]

Nice sir

[@neerajmathmaster8982]

Thanks.sir

[@mayureshargade8481]

Sir please create videos about partial differential equations ,pune university

[@imtiyazkhan469]

Sir please give me answer of this question. Why we Study Differential Equation.

[@imamhusain1287]

hello! sir,. ap bahut achha samjhate hai thanks sir lekin ek binti hai 'Polynomial Rings ' par video nahi mil rha hai.

[@shanezehra7597]

thnku so much sirrr you r so lovely

[@rekhagadhveer2101]

Sir MSc ki maths nhi krvaye kya you tube pr

[@fiziijaz8661]

Product of 2 prime may not prime then Theorem may is baat ko ly k agy kesy chala ja sakta hy

[@apurbakantiadhikary8107]

If P IS A ODD PRIME,1+(1/2)+(1/3)+...(1/P-1)=a/b prove that a is divisible by p

[@manuraj8375]

Composite number is multiplication of two prime number ,how sir 8 =2×4

[@suruk2688]

Didn't like the speed of the lecture as my sister is novice to BCA. Plus the speed is more for himself rather than students. Unhappy as she couldn't understand or process anything.

[@shubhamdesai5669]

Finally someone said it

[@_saksham_27]

Mai to 1.5 * pe dekhta hu 💀

[@ankitdahiya5952]

Decrease its own from play speed

[@_saksham_27]

@@ankitdahiya5952 Aree pehle se hi itna slow h....aur pta nhi kitna slow chahiye inhe.....time waste hoga slow me dekhne pe 😭

[@only_eyes]

.5 pe dekh lo

[@cvraman5908]

Sir in our without zero divisor the condition is ab=0 either a=0 or b=0 but in our multiplication modulo 3 there is 1*2=2 it become like this ab#0 s.t a#0 and b#0 ,which doesn't satisfie s our condition ,so how it become integral domain

[@nandinivarshney8313]

I am also confused here

[@abyron6417]

Yeah .....that's why I came to comment section

[@adksongs1524]

Bro please un no ko dekho jinka multiple 0 aa rha hai ,or usme se ek no = 0 hai that is the reason

[@adksongs1524]

I am confused in 1st theorem ,how multiply of 2 prime no is a prime no,

[@Himanshu_30_06]

@@adksongs1524 brother a=4 and b=2 multiplication modulo is 4 product is 0 but a#0 b#0

[@irrational2sim]

P=P1 multiplication modulo p P2, please help me understand this expression

[@anuradhabhandari2942]

Here p is composite no and multiplication of two prime no p1&p2 is composite no.

[@amanbhati4719]

Hey @@anuradhabhandari2942 you are right but here the problem is that its not simple multiplication operation it is multiplication modulo of p. If we multiple p1 and p2 then divide by p then its modulo will come 0 but here sir wrote that it will come equal to 'p'.

[@nehayadav9304]

(2) *4 (4) is not possible as z4 =( 0,1 ,2,3) . Little bit confuse

[@nikhilyadav3256]

great teaching

[@midnightsthought7704]

Sir iit jam ke liye linear Algebra ki videos kb aayegi sir We are waiting for that videos

[@ujjwalyadav8780]

Sir plz use board and chalk

[@joframorgan5740]

Sir pls explain theorem again.. we can't understand

[@mathsclassbymeeraltaf6808]

Very nice sir

[@fadiyarani2471]

Sir plz ring of real quanternions pa lecture dejiye

[@siddheshthakur8079]

Thanks

[@tanishagupta9934]

Sir, theorem samajhate waqt aapne shyad galat example le liya tha 2(×4)4 ...👉aisa hona chahiye 2(×4)2 Because multiplication (mod4 ) ke table me 0 se 3 tk ke hi numbers hote hain🤔

[@nishantsinghparihar3023]

12:10 sir got confused at this point and didn't explained why a or b should be zero.

[@manjukumari607]

Sir ko khud samajh me nahi aya aise hi jo likha tha bas bol diye

[@poreshtiwary1338]

Finite integral or integral domain me kya fark h 🤔

[@rohitashgurjar715]

Thanks sir

[@darpankumarthakur9826]

Sir I Think that you should learn more Good way of teaching because as you are teaching it is more Confusing and hard to understand a easy topic ,when you teach you make complicated to each problems

[@sikanderaliabro110]

Sir ap boht jaldi jaldi batate ja rhe hen,,,

[@uniqueacademyghotki9361]

Sir ,ap ne kaha k without zero divsor men two non zero ka product zero ho then 1x2 =2 Hy zero tu nhn Hy . Sorry

[@tayybarana8661]

Itni speed...aese jesay experts k agay present kr rhy hn

[@PriyankaGupta-gn9we]

Thank uu sir

[@UmeshKumar-jr4dm]

Sir app pahle best padhte hai

[@ajaykumar-gb3pb]

Sir Euclidean domain samajhea

[@ARkumar-nz9qs]

Thnks sir

[@animesh06]

Nice

[@priyaacharjee9360]

Sir need geometry 3d videos

[@bikasgauda5956]

Plz upload next video

[@niranjansahoo4748]

Example 2 me without 0 divisor wrong bol rahe he app.

[@unknowngarbage9428]

Prime number is prime number!!! 10:21 kuch samjh nhi aya

[@ashishmishraji]

Sir vo jo video k beech me subscribe ka sound aata hai....bell wala vo kafi distracting hai... Focus hta deta hai

[@mathsloversjn3453]

Nc sir

[@MathematicalMinds]

Why zero ring is not integral domain However it has without zero divisor property

[@surajkumargupta7309]

Sir thoda speed kam kriye plz

[@AnkitKumar-cr3qs]

Yes bhot tej pdhate hnn

[@kv-gw6bf]

Sir muje 1 ex solution kar dege? ???