Algebra Volume-4 Field Theory, I.S.Luther, I.B.S.Passi

 Algebra Volume-4 Field Theory, I.S.Luther, I.B.S.Passi

In this book, chapters divided in 4 parts. there are describing below:

Chapter 1 Algebraic Extensions .is briefly described an Algebraic Extensions. we study extensions of isomorphisms, Splitting fields, normal extensions, cyclotomic polynomials ,finite fields and separable and inseparable extensions.

Chapter 2 Galois Theory. here we prove three principal theorems. Namely:

1. The fundamental theorem of Galois Theory on the 1-1 corresponds between the sub-extensions of Galois extensions and closed subgroup o Galois group.
2. The fundamental theorem of Galois Theory on soluability of equations by radically soluability of equations by radicals of irreducible equations of prime degrees
3. Dedekind's theorem on linear independence of homomorphisms

Chapter 3 Algebras. in this, product of algebras, extensions of their scalar rings, composites o field extension

Chapter 4 further field theory ,in this proven the following 

1.the Nullstellensatz of Hilbert along a group of related theorems

2.the basic results about heights and depths of prime ideal in finitely generated over domains of fields.

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