Ring Theory | Elementary Properties of a Ring | (R, +, .) | Commutative Ring with Unity Examples

DISCRETE STRUCTURES AND THEORY OF LOGIC
UNIT-4
MATHEMATICS-3 (MODULE-3)
ABSTRACT ALGEBRA PLAYLIST
ALGEBRAIC STRUCTURES, GROUP, SUBGROUP, RING AND FIELD
DISCRETE MATHEMATICS
LECTURE CONTENT:
GROUP THEORY DISCRETE MATHEMATICS
CONCEPT OF RING
DEFINITION AND EXAMPLES OF RING
RING WITH UNITY
RING WITHOUT UNITY
COMMUTATIVE RING EXAMPLES
ELEMENTARY PROPERTIES OF RING
ring theory, ring theory important questions, ring theory abstract algebra, ring in group theory, elementary properties of a ring, what is ring, concept of ring, commutative ring, commutative ring with unity, commutative ring without unity, commutative ring examples, non-commutative ring with unity, ring of integers, ring of real number, ring of rational numbers, properties of ring, examples of ring theory, definition and examples of rings.
(COMMUNICATION LINKS)
1. TH-cam CHANNEL LINK:
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By: Dr. Anuj Kumar
Assistant Professor (Mathematics)
Ph. D, Gold Medalist in M. Sc and B.Sc.
National Fellowship (JRF & SRF) Holder During Ph. D.
DISCRETE STRUCTURES AND THEORY OF LOGIC MODULE-2
ALGEBRAIC STRUCTURES
KSC303
DISCRETE MATHEMATICS
GROUP THEORY
GROUP, SUBGROUP, RING & FIELD
ALGEBRAIC STRUCTURE IN DISCRETE MATHEMATICS
ALGEBRAIC STRUCTURE PLAYLIST
ALGEBRAIC STRUCTURE IN DISCRETE MATHEMATICS PLAYLIST
DISCRETE STRUCTURES AND THEORY OF LOGIC UNIT 2 PLAYLIST
DISCRETE MATHEMATICS PLAYLIST
DISCRETE MATHEMATICS FULL COURSE
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE
DISCRETE MATHEMATICS BTECH 2ND YEAR
DISCRETE MATHEMATICS BSC 1ST YEAR
DISCRETE MATHEMATICAL STRUCTURES
DISCRETE MATHEMATICAL STRUCTURES FOR COMPUTER SCIENCE
DISCRETE STRUCTURES COMPUTER SCIENCE
DISCRETE STRUCTURES UNIT 2
DISCRETE STRUCTURES MODULE 2
DISCRETE STRUCTURES LECTURES
DISCRETE STRUCTURES PLAYLIST
DISCRETE STRUCTURES AND THEORY OF LOGIC AKTU
DISCRETE STRUCTURES AND THEORY OF LOGIC BTECH 2ND YEAR
DISCRETE MATHEMATICS UNIT 2
DISCRETE MATHEMATICS MODULE 2
DISCRETE STRUCTURES AND THEORY OF LOGIC SYLLABUS AKTU
DISCRETE STRUCTURES FOR COMPUTER SCIENCE
DISCRETE STRUCTURES FOR COMPUTER SCIENCE BTECH 2ND YEAR
DISCRETE MATHEMATICS FOR BCS 1ST YEAR
DISCRETE MATHEMATICS AND GRAPH THEORY
DISCRETE MATHEMATICS AKTU
DISCRETE MATHEMATICS PLAYLIST AKTU
ABSTRACT ALGEBRA PLAYLIST
GROUP THEORY DISCRETE MATHEMATICS
GROUP THEORY ABSTRACT ALGEBRA
GROUP THEORY DISCRETE STRUCTURE
GROUP THEORY BSC 2ND YEAR
ABSTRACT ALGEBRA DISCRETE MATHEMATICS
BY DR. ANUJ KUMAR SIR
BY ANUJ KUMAR SIR
@FEARLESS INNOCENT MATH
#mathematics3 #discretestructure #kcs303 .

[@najeeb2973]

The best video on TH-cam about the concept of Ring.All my doubts are clear And your teaching method is very Good.Thank u so much sir.
JazakAllah ❤

[@dr.anuj.fearlessinnocentmath]

Most welcome dear 💖💖

[@AadilKhan-od4pl]

00:12 Rings and Elementary Properties
03:26 Ring Theory properties and distributor laws
08:41 A ring satisfies specific properties including commutative and existence of identity
11:34 Properties of a Ring
17:24 Commutative ring with unity and its 10 properties
19:53 Property of multiplicative identity determines unity in a ring.
25:29 Additive inverses in ring theory
28:46 Properties of Rings
36:37 Launch matrix forms a non-commutative ring

[@dr.anuj.fearlessinnocentmath]

Nice dear 💖💖

[@apt1682]

Thanks sir ur best teacher 😊

[@dr.anuj.fearlessinnocentmath]

Thanks dear

[@priyanshusharma9059]

Bhot bhot shukriya sir hame accha marks lane ka capable bnane ke leya

[@dr.anuj.fearlessinnocentmath]

Thanks dear

[@shikhasingh2196]

Thank you for the amazing explanation.

[@dr.anuj.fearlessinnocentmath]

Welcome dear💖💖

[@AbdulBasit-ox1wq]

Nce

[@dr.anuj.fearlessinnocentmath]

Thanks

[@alokindori1043]

20:10 Sir ring identity to hogi na.. Hum identity proof krne ke Liye addictive operation laga rhe h to ye to a+0=a proof Ho jayega ...

[@yoriichi7626]

And one more doubt sir Jo ring with unity hai aur jo commutative ring with unity hai unme hame bas multiplication leke hi proof karna hai kya ? Addition nhi use kar sakte ? Kyu ki 18:15 mai Jo question hai usme hai ex 4 usme toh likha hai + and . Toh kya hame dono use karne hai ya bas multiplication ??

[@dr.anuj.fearlessinnocentmath]

Yes kyonki
addition me hum sabhi property proof ker chuke hai
Isiliye multiply me hi
Unity
Commutative
Dikhate hai

[@yoriichi7626]

@@dr.anuj.fearlessinnocentmath ok sir thank you sir

[@niru_bhai8415]

Sir.... Har maths ki tarah dstl ka bhi important topics 10 marks wali video.jaldi banaiye....Sir PUT aane wale hain🙏🙏🙏

[@dr.anuj.fearlessinnocentmath]

Ok dear

[@yoriichi7626]

Sir 18:15 mai Jo do questions aapne diye hai sir unme toh bas hame inverse and commutative law hi toh proof karna padega na ? Kyuki question mai toh voi bola hai ki proof that it's commutative ring lekin aap khe rahe ki 10 property karni padegi proof kyu sir esa kyu karenge? Pls bataiye sir

[@dr.anuj.fearlessinnocentmath]

Pehle to ring proof karenge na
Jab ring proof ho jayega tabhi hum extra property ko add karte hai

[@yoriichi7626]

@@dr.anuj.fearlessinnocentmath ok sir thank you sir aapse acha koi padhata hi nhi hai sir thank you so much

[@yoriichi7626]

Sir ek question hai Mera ki iss unit se questions kese aayenge? Theorems aayenge kya proof karne ko? Ya kaise ayenge mujhe samjh nhi aarha questions kese ayene iss unit se pls batay sir

[@dr.anuj.fearlessinnocentmath]

Definition
Example
Theorem
Ye teeno aate hai

[@yoriichi7626]

​@@dr.anuj.fearlessinnocentmathok sir thank you sir you r the best

[@sandeepkumartiwari8436]

sir CRU ma 2 property aati hai tho HW ka question ma 10 property ku hold krya ga or exam ma bhi aisa he kara ga??????????????????

[@dr.anuj.fearlessinnocentmath]

CRU se pehle ring hona chahiye, cru to baad ki baat hai dear❤

[@Brijeshkumar_14]

Thanks

[@dr.anuj.fearlessinnocentmath]

Welcome dear