A Companion to Lang's Algebra

-- wherein can be found corrections, commentary, and divers supplementary material to the abovenamed book.

The links are to PostScript files. (Since the source files are not TeX but locally enhanced troff, I can't provide TeX or dvi files.)

Pp.1-46, Introduction, and Notes to Chapter I (Groups. Pp.ix-x, 1-74 of Lang)

Pp.46-90, Notes to Chapters II, III.1-7, IV.1-4, 6 (Rings, Modules, Polynomials. Pp.83-194 of Lang)

Pp.91-134, Notes to Chapters V, VI.1-11, 14, VIII.1, X.4, (XII.1) (Algebraic Extensions, Galois Theory, Transcendence Bases, and Nakayama's Lemma, plus one note on Absolute Values. Pp.225-303, 355-357, 424-426, and 466 of Lang)

Pp.134-164, Notes to Chapters XIII.1-7, XIV, XVI (Matrices and Linear Maps, Representations of One Endomorphism, The Tensor Product. Pp.503-536, 553-570 and 601-639 of Lang)

Pp.165-167, Notes to Appendix 2 (Some Set Theory. Pp.875-892 of Lang)

Pp.168-210, Exercises (supplementing those in Lang, and corrections and clarifications to a few of Lang's exercises)

Pp.211-222, Errata to past printings of Lang, and minor errata to the current printing

Supplementary materials

When I teach Math 250, I have the Companion printed and bound at Copy Central, 2560 Bancroft, for those who would like to buy it in hardcopy, and I include at the end the five items below.

The Axiom of Choice, Zorn's Lemma, and all that. 4pp.

A principal ideal domain that is not Euclidean, developed as a series of exercises. 1p.

Luroth's Theorem and some related results, developed as a series of exercises. 2pp.

Solution in radicals of polynomials of degree _<4, developed as a series of exercises. 2pp.

Quadratic reciprocity, developed from the theory of finite fields as a series of exercises. 2pp.

(There are some additional handouts that I often use in teaching Math 250B. Links to those are given, along with the above links, on this page.)