Intersection of two subring is a subring - Theorem - Ring Theory - Algebra

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Intersection of two subring is a subring. And it can be extended to any number of subgroups. It means Interection of arbitrary family of subring is a subring.
, i will explain this Theorem in today's video .
which is a very important topic of Ring Theory
everything is explained in Hindi
welcome you all in my channel LEARN MATH EASILY
This video will be very useful if you are student of Higher Classes in mathematics like B.Sc, M.Sc , Engineering and if you are preparing for UGC Net and iit Jam etc.
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Before this topic i did various other topics of Real Analysis:
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• Lower Bound, GLB and I... cyclic vbv

[@uttamsahu5168]

Tq❤ maam this video is very useful for me

[@abhinandanjain2399]

Thank you so much mam.

[@SakshiKumari-ud6hz]

Thanku mam🤗

[@tanmaysingh7071]

Mera kehna ye hai ki agar basis ke (n-1)koi bhi elements agar koi bhi nth element ko span kar rahe hain to sabko ek side le jaane par basis ke saare elements (jo ki sub set bhi hai) ka linear combination hoga .aur us linear combined me saare scalers zero nahi hain to wo LD hua lekin basis me es subset ko LI kaha gaya hai ...this is my question

[@iqra-aesthetic]

Sir u r genius

[@learnmatheasily]

Thanks

[@tanmaysingh7071]

Mam got my answer mere questio me jo zero aa raha hai wo normal zero hai(sabko ek side pe karne ke baad) lekin jis zero ka spanning ham LD ya LI me karte hain wo vector space ka zero hota hai so LI ya LD ka definition mere question me nahi lag sakta.

[@learnmatheasily]

Ok.

[@tanmaysingh7071]

basis me jo elements honge vo vector space me bhi honge .agar basis vector space ke har elements ko span kar sakta hai to basis ke bhi element ko generate karega ..let basis ke elements basis ke ek vector "a" ko generate kar rahe hain to sabko jab ek side pe le jayenge to wo linear dependent ho jayega.

[@learnmatheasily]

Aap confuse ho rahe ho spanning anf linear independence me. Ek baar aap inse related videos fir se dekho

[@tanmaysingh7071]

@@learnmatheasily basis poore vector space ko span karte hain na,to wo apne elements ko bhi span karenge.... true because wo bhi vector space ke elements honge.maine basis ka element "a" esliye liya kyunki agar ham basis ke bahar ka element lete to sabko ek side par le jane par wo basis ke elements ka linear combination nahi hota (bhale hi LI and LD me difinition basis par based nahi hai ,wo simple vector space ke finite elements ke subset par based hai lekin usi subset ko jab wo LI ho jata hai aur vector space ko span karta hai to basis ban jata hai ....am i right......please dont think that i am some thing else ...mujhe bahut dikkat hai esme....i am in 2nd year aur my sir didn't answered)

[@learnmatheasily]

Yes true

[@tanmaysingh7071]

Mam ek question hai -agar basis linear independent hota hai i.s all scalers of linear combination of linear independent set is zero to fir wo kaise kisi vector space ko generate kar sakta hai, for eg. Basis

[@learnmatheasily]

Agar linear combination khud hi zero he to saare scalars zero honge

[@tanmaysingh7071]

@@learnmatheasily to basis me jo elements honge vo vector space me bhi honge .agar basis vector space ke har elements ko span kar sakta hai to basis ke bhi element ko generate karega ..let basis ke elements basis ke ek vector "a" ko generate kar rahe hain to sabko jab ek side pe le jayenge to wo linear dependent ho jayega.

[@learnmatheasily]

Aap ek kam karo. Mere basis wale videos dekho. Kunki aap confuse ho ro he

[@becreative7522]

Mam integral domain ka video bna diya h ya pending h?

[@learnmatheasily]

Pahut pehle bana diya. Check playlist

[@jain443mohit]

mam ye iitjam k syllabus main h kya

[@learnmatheasily]

You hVe to tally your syllabus first

[@himanshisawaniya0825]

Explain well but mere dimag m ni aya kuch😞