# Math 421-01: Algebraic Structures

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- Syllabus
- Writing Guidelines
- Homework:
**Due 8/31:** Write up solutions to "Symmetries of the square" and "Properties of structures"
**Due 9/7:** Page 54, #2; Page 54, #3, 11; Page 37, #2.
**Due 9/14:** Page 54, #9, 14, 15, 16
**Due 9/21:** Page 67, #2, 8 (note the definition of U(n) on page 49), 12, 43.
**Due 10/1:** Page 67 #10, 30, 28, 33; Page 82 #4, 10, 22, 60
**Due 10/15:** Page 112, #4, 6, 8, 13, 50, 54
**Due 10/29:** Page 132 #4, 6, 10, 20, and prove that a group homomorphism is injective if and only if its kernel is the trivial subgroup; p. 134 #35, 36, 38.
**Due 11/5:** Page 148 #1, 4, 10, 13, 15
**Due 11/19:** Let G be an Abelian group, with H a subgroup of G. Prove that H is normal.
**Due 11/26:** Page 191 #1, 2, 4, 48
**Due 12/3:** Page 165 #2, 5, 8, 68 (for the last, read pp. 159--165); p. 194 #52
**Due 12/10:** Page 240 #2, 3, 20, 22, 40; Prove that in any ring, the additive identity has no multiplicative inverse; p. 254 #4, 18, 24, 36, 50.

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Wesley Calvert
Department of Mathematics & Statistics
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Murray State University
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