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Algebra by Dr. Pankaj Kumar

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Algebra written by Dr. Pankaj Kumar . This is an other book of mathematics cover the following topics.

  • Subnormal and Normal series-I
    OBJECTIVE, INTRODUCTION, SUBNORMAL AND NORMAL SERIES, ZASSENHAUS LEMMA AND SCHREIER’S REFINEMENT, THEOREM, COMPOSITION SERIES, COMMUTATOR SUBGROUP, MORE RESULTS ON COMMUTATOR SUBGROUPS, INVARIANT SERIES AND CHIEF SERIES, KEY WORDS, SUMMARY, SELF ASSESMENT QUESTIONS, SUGGESTED READINGS.
  • Central series and Field extensions-I
    OBJECTIVE, INTRODUCTION, CENTRAL SERIES, NILPOTENT GROUPS, SOLVABLE GROUP, SOME DEFINITIONS, FINITE FIELD EXTENSIONS, PRIME FIELDS, KEY WORDS, SUMMARY, SELF ASSESMENT QUESTIONS, SUGGESTED READINGS

  • Field Extensions-II and constructions
    OBJECTIVE, INTRODUCTION, ALGEBRAIC EXTENSION AND TRANSCENDENTAL EXTENSIONS, ROOTS OF POLYNOMIALS, SIMPLE EXTENSIONS, CONJUGATE ELEMENTS, CONSTRUCTION BY STRAIGHT EDGE AND COMPASS, KEY WORDS, SUMMARY, SELF ASSESMENT QUESTIONS, SUGGESTED READINGS

  • Field Extensions-III STRUCTURE
    OBJECTIVE, INTRODUCTION, ALGEBRAICALLY CLOSED FIELD, MORE ABOUT ROOTS, SEPARABLE EXTENSIONS, SOME DEFINITIONS, SYMMETRIC RATIONAL FUNCTIONS, NORMAL EXTENSION, KEY WORDS, SUMMARY, SELF ASSESMENT QUESTIONS, SUGGESTED READINGS.

  • Galois Theory and Finite Fields
    OBJECTIVE, INTRODUCTION, PERFECT FIELD, GALOIS THEORY, SOLVABILITY BY RADICALS, CYCLOTOMIC POLYNOMIALS, FINITE FIELDS, KEY WORDS, SUMMARY, SELF ASSESMENT QUESTIONS, SUGGESTED READINGS

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