MATH 4321 HOMEWORK (Spring 2009)

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Book = A First Course in Abstract Algebra, 7th Ed, by J. B. Fraleigh, Addison-Wesley.
Note that there might be more than one correct answer for any given question.

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1/20 Read lecture notes & do Sec 18 pgs 174/5: 1, 3, 5, 7, 9, 11.  Submit 1/29
1/22 Read lecture notes & do Sec 18 pgs 175/6:  14, 16, 19, 20, 31, 27, 
     38, 46, 22, 23, 40.  Submit 1/29
     Read pages 167-174 & pages 177-182.  
1/27 UTA closed due to weather.
1/29 Read lecture notes & pgs 177-9 including Def 19.6 & do 
     Sec 19 pgs 182/3: 14, 23(& extend question 23 to apply to integral domains), 24, 28. 
     Submit Feb 10.
2/03 Read lecture notes & Sec 19 & do Sec 19 pgs 182/3: 5-11, 27, 29, & extend question 23 to 
     apply to domains that are not integral domains.  Submit Feb 10.  
2/05 Read lecture notes & Sec 20 & do Sec 20 pgs 189/90: 1, 5, 11, 13, 24,
     23(justify answers to 23 (e.g., pg reference or theorem or counterexample)).
     Submit Feb 10.  
2/10 Read lecture notes & Sec 21 & do Sec 21 pgs 196-7: 1, 2, 7, 8, 12, 14. 
     Submit Feb 17.  
2/12 Read lecture notes & Sec 22 & do 
     Sec 22 pgs 207-8: 1, 4, 6-8, 14, 20, 22, 25. 
     Submit Feb 17.  
2/17 Read lecture notes & Sec 23 & do 
     Sec 23 pgs 218-220: 4, 35, 36, 6, 9, 27, 28, 34.
     Submit Feb 24.  
2/19 Test 1 today -- no new homework assigned.
2/24 Read lecture notes & Sec 23 & do 
     Sec 23 pgs 218-220: 14, 16, 18.
     Submit Mar 3.
2/26 Read lecture notes & pgs 224.5-226 & Sec 26 & do 
     Sec 24 pgs 226-7: 14, 5, 4, 6, 10.
     Sec 26 pgs 243-5: 29, 2, 17, 37.
     Submit Mar 3. 
3/03 Read lecture notes & Sec 26 & do 
     Sec 26 pgs 243-5: 18, 4, 12, 14, 22(a)(c), 24-26.  
     Submit Mar 10. 
3/05 Sec 27 pgs 252-4: 1 (max ideals only), 2 (max ideals only), 34, 35, 37.
     Submit Mar 10.   
3/10 Learn box on pg 248. Read Thm 27.17 & its proof. Read prime fields pg 249-250.
     Sec 27 pgs 252-4: 1 (prime ideals), 2 (prime ideals), 24, 14(a)(b)(f) (justify). 
     Submit Mar 24. 
3/12 Read last 2 paragraphs on pg 251 and read pg 252.  Do Sec 27 pgs 252-4: 31, 5, 6, 30.
     Submit Mar 24.
3/17 SPRING BREAK
3/19 SPRING BREAK
3/24 Read lecture notes & Sec 29 & do 
     Sec 29 pgs 272-4: 1, 2, 4, 6(Hint: E. Criterion), 11-15, 21, 27.
     Submit Mar 31.
3/26 Test 2 today -- no new homework assigned.
3/31 Sec 29 pgs 272-4: 18, 30, 31. 
     Submit April 7.
4/02 Read lecture notes & Sec 30 & do 
     Sec 30 pgs 280-2: 15(a)-(d) (justify), 25 (note: "transformation" = "map").
     Submit April 7.
4/07 Sec 30 pgs 280-2: 1, 2, 4, 6, 7, 19.
     Submit April 14.
4/09 Read lecture notes & pgs 283-289 & do
     Sec 31 pgs 291-2: 1-3, 5, 7, 9, 11, 13, 19(a)-(c), 22, 28, 29.
     Submit April 14.
4/14 Read lecture notes & Sec 33 & do
     Sec 33 pgs 304-5: 8(a),(g)(justify), 11, 1, 4, 8(c)(justify).
     Submit April 21.
4/16 Read lecture notes & Sec 48 & do
     Sec 48 pgs 422-4: 1-3, 7-11, 13, 25, 26, 28, 38, 15.
     Submit April 21.
4/21 Do Sec 48 pgs 422-4: 36(a)(b).
     Submit April 28.
4/23 Read lecture notes & Sec 49 & do
     Sec 49 pgs 430-1: 1-3, 7, 8(b)(d)(e) (justify), 13.
     Read lecture notes & Sec 50 & do
     Sec 50 pgs 434-6: 1-5, 14(a)-(e),(j) (justify), 18, 21.
     Submit April 28.
4/28 Test 3 today -- no new homework assigned.
4/30 Read lecture notes & Sec 51 & do
     Sec 51 pgs 442-4: 1, 4, 7, 8(a)-(g)(justify), 
                       9 (hint: use E = F(alpha, beta), 13, 15.
     Submit May 5.
5/05 Read lecture notes & Secs 53 & 56 & do
     Sec 53 pgs 454-6: 1-4, 8, 11, 13, 15(a)-(c),(e),(g) (justify).