Rings, Euclidaen domains, PIDs, UFDs, Factorization in Polynomial rings, Prime and maximal ideals, Chinese remainder theorem.

Field Theory: Field extensions, Fundamental theorem of algebra, Normal and Separable extensions, Splitting fields, Galois extensions, Galois group of a polynomial. Fundamental theorem of Galois theory, Solvabality by radicals, Transcendence bases.  


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Last updated: 20 May 2024