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Abstract Algebra

Abstract Algebra. By S. Joshi. Content. Binary Structures & Group Subgroup Isomorphism Rings Fields. Source. Engineering Maths Cracking the Subject GRE Math by Princeton RAE GRE Math. Binary Structures & Group. Binary operation & structure Semi group Monoid Group

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Abstract Algebra

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  1. Abstract Algebra By S. Joshi

  2. Content • Binary Structures & Group • Subgroup • Isomorphism • Rings • Fields

  3. Source • Engineering Maths • Cracking the Subject GRE Math by Princeton • RAE GRE Math

  4. Binary Structures & Group • Binary operation & structure • Semi group • Monoid • Group • Examples of group (all, imp from exam point of view) • Example of groups • Cyclic (Klein four group or Viergruppe)

  5. Subgroup • Cyclic Sub group (complex number) • e • Monoid (with inverse ) • Generator and relation • Some theorems • Binary property / commutative (Albean)

  6. Example • General Linear Group

  7. Multiplication Table

  8. Additive group of integers modulo n

  9. Finite Abelian group

  10. Isomorphism • Classification of finite abelian group • Group homomorphism • Types of morphoism • Many questions

  11. Rings • Three properties • Example • Ring homomorphism

  12. Integral Domains

  13. Fields • Unit

  14. References • Cracking the subject GRE Math

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