This is a list of typos in Lang's book that was compiled by a student in
Math 250A at the end of the Fall, 1992 semester.  It is quite possible
that many of these have been corrected in recent printings of the book;
when I taught this course in 1992, the third edition of "Algebra" had
just come out.

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General comment: I prefer the "underbar" on the set inclusion symbol when the 
intention is that one set contains *or is equal to* another set.

(Note: To compute line numbers, I have counted a diagram as one line.)

p. 6, line -21: replace "H or G" by "H of G"

p. 17, line 2: replace "G/K into G/H" by "G/K onto G/H"

p. 19, line 14: replace "dagonal" by "diagonal"

p. 19, line 24: what is "g" in "r >= g"?

p. 26, line 4: replace "x(yx)" by "x(ys)"

p. 26, line 5: replace "es = e" by "es = s"

p. 26, line 13: replace "yxy^-1" by "xyx^-1"

p. 27, line -12: replace "normalizer" by "centralizer" (I'm not sure about 
  this one)

p. 29, line 14: replace "G = \prod Gs_i" by "S = \coprod Gs_i"

p. 29, line -8: replace "we called" by "we call"

p. 30, line -3: replace "\pi(\tau)f(x_{\sigma(1)}, \dots , x_{\sigma(n)})" by 
    "\pi(\sigma)f(x_{\tau(1)}, \dots , x_{\tau(n)})"

p. 34, line 15: replace "that G has a" by "G has a"

p. 36, line 10: replace "is H be assumption" by "is H by assumption"

p. 36, line 15: replace "p, q be the distinct" by "p, q be distinct"

p. 36, line 15: replace "distinct porimes" by "distinct primes"

p. 37, line -11: What does "0" mean?  Should it be the set "{0}"?  This occurs
    in many subsequent places.

p. 39, line -14: replace "by the element of T" by "by the elements of T"

p. 42, line -14: replace "The A(p) is" by "Then A(p) is"

p. 42, lines -2, -3, -4: exchange "p" and "q" everywhere

p. 42, line -3: replace "= 1," by "= 0,"

p. 53, line -17: replace "Mor(B,C) x Mor(A, B)" by "Mor(A, B) x Mor(B, C)"

p. 53, line -12: exchange "left" and "right"

p. 56, line -15 (middle diagram): replace "A'" in lower left corner by "A"

p. 56, line -14: replace "A" by "\cal A"

p. 56, line -7 (lower diagram): what is "[h]"?  What are the brackets for?

p. 60, line 17: replace "x' on x" by "x' to x"
 
p. 61, line -7: replace "Exercises 50-58" by "Exercises 50-56"

p. 62, line 3 (top diagram): this diagram has many mistakes 

p. 62, line 14: replace "their coproduct is" by "their product is"

p. 63, line 11: replace "gorups" by "groups"

p. 68, line 10 (top diagram): replace "\lambda_*" by "(f_{s'} \circ \lambda)_*"

p. 72, line 14: I think the statement of this proposition is flawed.

p. 75, lines -12 and -16: I find this notation difficult.  What are the 
   unions ranging over?

p. 76, line 14: replace "(x_1 x_2 ^{\psi(h_1)}" by "(x_1 x_2 ^{\psi(h_1)(x_2)}"
 
p. 77, line 15: replace "finite grop" by "finite group"

p. 81, line -13 (exercise 54): The G_i should generate G

p. 88, line -2: replace "as additive" by "as an additive"

p. 93, line -7: regarding "every ideal is principal", what about n=0?

p. 96, line -11: replace "the endomorphisms" by "the endomorphism"

p. 108, line -1: replace "\phi(a) = a/1" by "\phi_s(a) = a/1"

p. 118, line -8: replace "that A_{tor} is" by "that M_{tor} is"

p. 120, line 3: replace "section 4" by "section 3"

p. 124, line -3: replace "space over K," by "space over K."

p. 128, line 19: replace "Proposition 9.1" by "Proposition 7.1"

p. 136, line 12: replace "as A-module" by "as A-modules"

p. 137, line 7: replace "Chapter I, section 9" by "Chapter I, section 7"

p. 147, line 7: replace "M = M_r" by "M_{r+1} = M_r"

p. 153, line 15: replace "for M as linear" by "for M as a linear"

p. 158, line -13: replace "Let z \in Ker d''" by "Let z'' \in Ker d''"

p. 162, line 16: replace "complete disctete" by "complete discrete"

p. 168, line 2-4 (exercise 10a): missing subscript "p" in 5 places

p. 229, line -11: replace "\alpha_0 + \alpha_1" by "a_0 + a_1"

p. 232, line 17: replace "Let E" by "Let L" (I'm not sure about this one)

p. 239, line 12 (diagram): top arrow should point from L to L'

p. 241, line 12: replace "By Theorem 4.1" by "By Corollary 4.2"

p. 241, line -6: replace "a_i_n)" by "\alpha_i_n)"

p. 254, line 2: What is "K"?