Course Contents
Rings and Subrings. Division rings. Polynomial Rings. Matrix Rings. Homomirphism. Ideal and Factor Rings. Prime Ideals and Maximal Ideals. Nilpotent elements. Divisors, Units and Associates. Divisibility theory of Integral Domains. Unique Factorization Domains. Principal Ideal Domains. Euclidean Domains. Field Extensions. Algebraic and Transcedental elements. Algebraic Extensions. Factorization of Polynomials. Modules and Submodules. Homomorphisms and Quotient Modules. Decomposition of Modules. Finitely Generated Modules. Torsion Modules. Free Modules. Basis Rank. Exact Sequences. Injective and Projective Modules. Noetherian and Artinian Modules
Module, an Introduction
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Noetherian and Artinian Modules
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Properties of Noetherian and Artinian Modules
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Exact Sequence
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Operations on Modules
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Colon and Radical of Ideals
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Homomorphism of Modules
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Book Title : Topics in Algebra
Author : I. N. Herstein
Edition : 2nd Edition
Publisher : JOHN WILEY & SONS, INC
Book Title : Abstract Algebra
Author : David S. Dummit & Richard M. Foote
Edition : 3rd Edition
Publisher : JOHN WILEY & SONS, INC
Book Title : A First Course in Abstract Algebra
Author : John B. Fraleigh
Edition :
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Title : A First Course in Abstract Algebra by John B. Fraleigh
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Title : Topics in Algebra by I.N. Herstein
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Title : Abstract Algebra by David S. Dummit & Richard M. Foote
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