A
First Graduate Course in Abstract Algebra, Errata, modified 7/05

Bill Wickless

page 12, Problems 1.3.5-1.3.7 should be moved to the fourth problem set.

page 34, Prob. 1.9.3 "Use Problem 1.8.4 ..."; Prob. 1.9.5 "Complete the proof of Lemma 1.9.1 ..."

page 43, Problem 1.11.1 "Prove Lemma 1.11.1..."

page 73, extra "proof" in Theorem 2.6.5

page 74, delete Problem 2.6.6

page 122, upper case V for the vector space

page 126, let F be the complex numbers in Problem 4.8.4.

page 132, Problem 4.9.1 "Example 4.9.5"

page 155, line 14 of proof, "minus e sub delta"; also in the proof of Th. 5.4.1 and in Problems 5.4.1,5.4.2 we need to use the fact that S is a directed set, not just a poset

page 173, Problem 5.7.5, "In the proof of Lemma 5.7.1..."

page 180, Problem 6.3.5, the ring R need to be specified, say that R is a field

page 181, Problem 6.3.8, "Prove that R is neither right nor left Artnian."

page 184, the given correspondence from transformations to matrices is just a ring isomorphism

page 190, delete the first (totally false) sentence, then delete the word "also" from the second

page 191, "the image of each map is the kernel of the next one"

page 192, line -4, -[lambda(g)+lambda(h)]

page 193, in the definition of the G-action we need an alpha in front of the a

page 210, line 3, "By Theorem 8.2.2...."

page 215, after Def. 8.5.2, "we have already noted in Problem 8.2.2..."

page 217, line 15, add the sentence "First note that G/H_g cannot be torsion-free, since then g is not in the subgroup <H_g,2g>, contradicting the maximality of H_g."

page 217, line 19, "and, since it is easy to prove that G/<H_g,g> must be a torsion group (check this), we have that G/H_g is torsion."

page 219, "we can invoke Lemma 8.5.1...".; replace t by k in the double subscript in line -14

Bill Wickless

page 12, Problems 1.3.5-1.3.7 should be moved to the fourth problem set.

page 34, Prob. 1.9.3 "Use Problem 1.8.4 ..."; Prob. 1.9.5 "Complete the proof of Lemma 1.9.1 ..."

page 43, Problem 1.11.1 "Prove Lemma 1.11.1..."

page 73, extra "proof" in Theorem 2.6.5

page 74, delete Problem 2.6.6

page 122, upper case V for the vector space

page 126, let F be the complex numbers in Problem 4.8.4.

page 132, Problem 4.9.1 "Example 4.9.5"

page 155, line 14 of proof, "minus e sub delta"; also in the proof of Th. 5.4.1 and in Problems 5.4.1,5.4.2 we need to use the fact that S is a directed set, not just a poset

page 173, Problem 5.7.5, "In the proof of Lemma 5.7.1..."

page 180, Problem 6.3.5, the ring R need to be specified, say that R is a field

page 181, Problem 6.3.8, "Prove that R is neither right nor left Artnian."

page 184, the given correspondence from transformations to matrices is just a ring isomorphism

page 190, delete the first (totally false) sentence, then delete the word "also" from the second

page 191, "the image of each map is the kernel of the next one"

page 192, line -4, -[lambda(g)+lambda(h)]

page 193, in the definition of the G-action we need an alpha in front of the a

page 210, line 3, "By Theorem 8.2.2...."

page 215, after Def. 8.5.2, "we have already noted in Problem 8.2.2..."

page 217, line 15, add the sentence "First note that G/H_g cannot be torsion-free, since then g is not in the subgroup <H_g,2g>, contradicting the maximality of H_g."

page 217, line 19, "and, since it is easy to prove that G/<H_g,g> must be a torsion group (check this), we have that G/H_g is torsion."

page 219, "we can invoke Lemma 8.5.1...".; replace t by k in the double subscript in line -14