DSC-14 RING THEORY

This playlist is useful for students enrolled in B.Sc. (H) Mathematics, B.Sc.(P) Physical sciences, Generic elective (Maths) etc. This is useful for CSIR UGC NET and IIT JAM also. https://www.youtube.com/playlist?list=PLOcyoCwR67V_VrlyLYW0WHTdmIGfTCFrT

Curated by: MATHS IDOL (46 videos)

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Currently Playing: Lec 16.1: (EASY EXPLANATION)Polynomial rings: definition and basics (Gallian)

Find complete playlist of ch-16: Polynomial Rings from BOOK GALLIAN. You can find the entire concept of this chapter in this playlist. https://www.youtube.com/playlist?list=PLOcyoCwR67V_VrlyLYW0WHTdmIGfTCFrT

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Tracks in this Playlist

• Lec17.9:(IMPORTANT) Construction of field with 8 elements and some more examples: Ch-17 Book Gallian
• Lec17.8 (IMPORTANT THEOREM FOR EXAMS)Thm 17.5: p(x) is irreducible iff ideal (p(x))is maximal
• Lec 17.7:(USEFUL EXAM QUESTIONS )Factorization of Polynomials: Q5, 15 of exercise ch-17 Book Gallian
• Lec 17.6:(VERY IMPORTANT) Eisenstein criterion: Thm 17.4 , Q13,14, eg 9 : ch-17 Book Gallian
• Lec17.5:(VERY EASY EXPLANATION)Thm 17.3 Mod p irreducibility test (Book gallian) IMPORTANT FOR EXAMS
• Lec 17.4: (EXAM THEOREM) Thm 17.2: Reducibility over Q implies reducibility over Z from GALLIAN
• Lec 17.3 : Gauss Lemma MADE SIMPLE: IMPORTANT FOR ABSTRACT ALGEBRA (Book Gallian ch-17)
• Lec 17.2 (Very Important Theorem)Thm 17.1: Reducibility test for polynomials of deg 2or 3 (GALLIAN)
• Lec17.1:(EASY EXPLANATION)Irreducible Polynomial with Eg1,2,3 of book Gallian Ch-17 Factorization..
• Lec 16.16 : (VERY IMPORTANT EXAM QUESTION)Polynomial Rings: Exercise Q44 (Gallian)
• Lec 16.15:(VERY IMPORTANT)Polynomial Rings: Exercise Q43 (Gallian)
• Lec 16.14: (EXAM QUESTION)Polynomial Rings Exercise Q42 (Book Gallian)
• Lec 16.13: (IMPORTANT EXERCISE QUESTION)Polynomial Rings: Exercise Q31(Book: gallian)
• Lec 16.12: (VERY VERY IMPORTANT) Z[x] is not a principal ideal domain(Gallian)Polynomial Rings Q26
• Lec 16.11 (IMPORTANT FOR EXAMS)Polynomial rings : Q20 of exercise of gallian
• Lec 16.10: (IMPORTANT)Polynomial Rings: Q9,19 of exercise (Book Gallian)
• Lec 16.9(EASY EXPLANATION) Char R=Char R[x](Book Gallian)Polynomial rings: Exercise Q4
• Lec 16.8 : (VERY USEFUL AND IMPORTANT)Polynomial rings: Exercise Questions 1 and 3(Gallian)
• Lec 16.7 (IMPORTANT FOR EXAMS)Polynomial rings Example 3(Gallian)
• Lec 16.6: (VERY IMPORTANT CONCEPT)Principal ideal domain, theorem 16.4 & 16.5,ch-16 Polynomial rings
• Lec 16.5: (IMPORTANT THEOREM)Polynomial Rings: Theorem 16.3 and complex roots of unity: Book Gallian
• Lec 16.4: (EXAMS:TWO IMPORTANT THEOREMS ) Factor theorem and remainder theorem from Book Gallian
• Lec 16.3 : (MADE EASY)Polynomial rings: Division algorithm &example 1 from Gallian
• Lec 16.2 : (VERY IMPORTANT THEOREM)Theorem 16.1: If Dis an ID then D[x] is also an ID.Book : Gallian
• Lec 16.1: (EASY EXPLANATION)Polynomial rings: definition and basics (Gallian)
• Lec-15.21: (IMPORTANT EXERCISE QUESTIONS) Solutions for Chapter 15 : Ring homomorphisms : Part-02
• Lec-15.20: (EXERCISE QUESTIONS MADE EASY)solutions for Chapter 15 : Ring homomorphisms : Part-01
• Lec- 15.19:(VERY IMPORTANT THEOREMS)Second isomorphism theorem, third isomorphism theorem for rings
• Lec-15.18: (VERY IMPORTANT CONCEPT)Field of Quotients : In Hindi
• Lec-15.17: (VERY VERY IMPORTANT)First isomorphism theorem on rings, ideals are kernels: in Hindi
• Lec15.16: (IMPORTANT TOPIC MADE EASY)Properties of Ring Homomorphism with proof, kernals are ideals
• Lec-15.15: (MADE SIMPLE)Ring Homomorphism: Definition and examples: In hindi
• Lec-14.14: (VERY USEFUL EXERCISE QUESTION)IDEALS AND FACTOR RINGS: EXERCISE OF CHAPTER 14: IN HINDI
• Lec14.13:(IMPORTANT THEOREM MADE EASY):EVERY MAXIMAL IDEAL IS A PRIME IDEAL IN A COMMUTATIVE RING...
• Lec-14.12: (IMPORTANT CONCEPT MADE EASY)PRIME IDEAL & MAXIMAL IDEAL: DEFINITION & EXAMPLES:IN HINDI
• Lec-14.11:(FULL CONCEPT IWITH EASY EXPLANATION))FACTOR RING : EXAMPLES OF DIFFERENT VARIETY:IN HINDI
• Lec-14.10: (IMPORTANT CONCEPT)FACTOR RING: Definition and existence of factor ring: IN HINDI
• Lec14.9:(IMPORTANT CONCEPT MADE SIMPLE)Ideal: Definition and examples: In hindi
• Lec14.8: (IMPORTANT DEFINITION)Characteristic of a ring: Examples and exercise questions: In Hindi
• Lec-14.7: (VERY IMPORTANT EXERCISE QUESTIONS)INTEGRAL DOMAIN: IN HINDI
• Lec-14.6: (EASY EXPLANATION)Integral Domain and its important Examples : In HINDI
• Lec 14.5: (SO EASY TO UNDERSTAND)Unit in a Ring: Definition, examples &related questions: IN HINDI
• Lec-14.4: (EASY EASY EASY)SUBRING: DEFINITION, SUBRING TEST WITH PROOF, EXAMPLES, EXERCISE QUESTIONS
• Lec-14.3: (EXAM ORIENTED)Domain of gaussian Integers, Properties of ring: In HINDI
• Lec-14.2: (EASY EXPLANATION FULL CONCEPT)ZERO DIVISOR, INTEGRAL DOMAIN, FIELD: Examples &theorems
• Lec-14.1:(FULL EXPLANATION)Ring : Definition and examples: IN HINDI