Stellar

Sets Naive set theory Definitions Basic results Relations Types of orders Examples Functions Basic results Set Cardinality Integers Principle of induction Exercises Construction of the integers Division Greatest common divisor Prime numbers Diophantine equations Exercises Modular Arithmetic Divisibility rules Exercises Euler's totient function Exercises Chinese remainder theorem Exercises Miscellaneous Exercises Binary operations Examples Monoids Introduction to monoids Submonoids Groups Introduction to groups Symmetric group Subgroups Exercises Generating set of a group Types of subgroups Geometric groups Cyclid groups Examples Permutations and k-cycles Exercises Cosets Isomorphisms Kernels Homomorphisms from cyclic groups Exercises Group actions Quotient groups Isomorphism theorems Exercises Direct and semidirect product Direct product Semidirect product Sylow theorems Exercises Fields Introduction to field Rings Introduction to rings Quotient rings Isomorphism theorems Commutative rings Noetherian rings Exercises Euclidean domains Unique factorization domains Ideal factorization in in ℤ[i√5]Quadratic rings Polynomials Polynomials over rings Valuations associated with prime elements Primitive polynomials Field extensions Modules Modules over a ring Submodules, morphisms and quotients Generators Torsion modules and cyclic modules Modules over PIDs Primary modules Socle and cyclic p-primary components Lattices

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