I will be taking abstract algebra course in a month from now. I am first time taking and algebra course and will be sitting with math majors. Can someone suggest me a book suitable for me i.e for beginner,inexperienced and lots of motivation as well as rigorous. I have A First course in abstract algebra by John Fraleigh in my mind. Can someone suggest similar or some more books or any material which will be helpful to me
Review of basics, Permutations, sign of a permutation, inversions, cycles and transpositions, groups, subgroups and factor groups, Lagrange's Theorem, homomorphism, normal subgroups, Quotients of groups, Cyclic groups, generators and relations, Cayley's Theorem, group actions, Sylow Theorems. Direct products, Structure Theorem for finite abelian groups. Simple groups and solvable groups, nilpotent groups; Free groups, free abelian groups. Rings, Examples (including polynomial rings, formal power series rings, matrix rings and group rings), ideals, prime and maximal ideals, rings of fractions, Chinese Remainder Theorem for pairwise comaximal ideals. Euclidean Domains, Principal Ideal Domains and Unique Factorizations Domains. Polynomial rings over UFD'; finite field and field extensions.