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

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This video lecture of Ring Theory | Integral Domain | Integral Domain Examples | Theorems / Definitions | Examples & Solution By Definition | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand following topic of Mathematics:
1. What is Integral Domain ?
2. Examples Of Integral Domain In Ring Theory
3. Theorem Based On Integral Domain
4. This is part Of Ring Theory and Abstract Algebra
#RingTheory #IntegralDomain #AbstractAlgebra
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This Concept is very important in Engineering & Basic Science Students. This video is very useful for B.Sc./B.Tech & M.Sc./M.Tech. students also preparing NET, GATE and IIT-JAM Aspirants.
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Time Stamp
Integral domain-
0:00 | An intro
0:18 | Topic introduction
3:21 | Integral Domain definition
5:14 | Example 1
6:26 | Example 2
8:14 | Theorem
12:43 | Conclusion of video
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Dr.Gajendra Purohit

[@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 🙏

[@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.

[@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 👑

[@fyadmohammed8856]

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

[@mustafaahmed920]

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

[@ashishshukla7144]

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

[@rajarammishra255]

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

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Thanks sir for everything you do selflessly 🙌

[@muhammadsaqibulhassan8400]

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

[@tanyasanjay9711]

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

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

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Great teacher, Love you sir

[@manoharsain434]

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

[@msuresh2756]

Super sir thank you Many doubts clear about integral domail

[@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.

[@monuchouhan4333]

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

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thank you sir for the wonderfull lecture

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Great work sir .

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

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Thanku sir for valuable lecture

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Sir love you and thank you so much you are best thanks a lot I can't explain my love you save my time with my family Money thank you so much love you ❤❤❤❤

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

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Thank you so much 💐.........sir

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

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Thank you Sir. 🙏 🙏

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Thanks sir..🙏🏻🙏🏻🙏🏻♥️ very helpful

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

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Thank you so much sir ☺️☺️

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Thank you sir, ap a66i samjhate ho. ❤

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Sir you are the best teacher

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

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thnku so much sirrr you r so lovely

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

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Howww are yu frnd shivi

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great teaching

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

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Thanks Sir 👍🏻👍🏻

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Thank you sir 😊🙏

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Thank you sir 😊

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Sir Real analysis ke opar video kab aayega?

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Best for learning

[@abhinandanjain2399]

Thank you sir.

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

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ThankYou Sir

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Nice sir

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Sir vector book ke chapter per video dalo sir plzzzzz

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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

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Is the ring theory applied mathematics

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@@Haseeb-if4yx pure.

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@@Haseeb-if4yx ring theory is pure mathematics

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This is pure mathematics bro

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IC lye Tu bichara fail huta rha😂

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Thanks.sir

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

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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?

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Best teacher the app

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Thanks sir

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Tnq..sir

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Very nice sir

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Sir you are best teacher of m

[@gautammishraarijitsingh18]

Mathematics

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Thanks sir 😇

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Thanks

[@funnykarty2107]

Thanks 😘

[@mehakbansal9701]

Sir pls complete lectures of ring

[@ADARSHKUMAR-qo9ye]

Bahut achaa sir

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Sir please upload video on Dynamics

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

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sir please make the video of field.

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

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JAI RADHESHYAM JI JAI HANUMAN JI

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Sir please create videos about partial differential equations ,pune university

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Sir ideal pr class le lijie please

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JAI GORISHANKAR JI JAI SIYARAM JI

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Thank uu sir

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

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Nice

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Thnks sir

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Sir congruence of triangle par video

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

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

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Sir plz ring of real quanternions pa lecture dejiye

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Plz upload next video

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

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Sir MSc ki maths nhi krvaye kya you tube pr

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Nc 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

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

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

[@joframorgan5740]

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

[@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!! ????

[@UmeshKumar-jr4dm]

Sir app pahle best padhte hai

[@sikanderaliabro110]

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

[@pritishalini202]

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

[@madhubarnwal..]

Ha

[@fiziijaz8661]

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

[@kv-gw6bf]

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

[@ajaykumar-gb3pb]

Sir Euclidean domain samajhea

[@ujjwalyadav8780]

Sir plz use board and chalk

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Sir need geometry 3d videos

[@manuraj8375]

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

[@nehayadav9304]

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

[@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

[@poreshtiwary1338]

Finite integral or integral domain me kya fark h 🤔

[@ashishmishraji]

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

[@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🤔