Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
abstract
before second test
| Question | Answer |
|---|---|
| additive identity | a+o=a |
| multiplicative identity | ax=1 |
| additive inverse | a+x=o |
| multiplicative inverse | [a][n]=1 |
| subring | ring closed under multiplication and subtraction |
| commutative ring | xy=yx |
| unity | multiplicative identity |
| units | ab=ba=1 (a is a unit) |
| zero divisor | R is a commutative ring, a does not equal 0, b does not equal 0, ab=0 |
| integral domain | commutative ring but has no zero divisors |
| field | commutative ring with unity in which every non-zero element is a unit |
| factor of a polynomial | something you can factor out with remainder 0 |
| root of a polynomial | plug in that number and get 0 |
| Theorem 8.1 | Suppose R is an integral domain and a,b,c are elements of R with a not equal to 0. If ab=ac, then b=c |
| Theorem 8.2 | A field has no zero divisors |
| Theorem 8.5 | Zn is a field iff n is prime |
| Theorem 8.6 | Let o less than x less than m. Then [x] is a unit in the ring Zm iff gcd (x,m)=1 |
| Theorem 8.8 | All finite domains are fields |
| examples of finite fields | Z5, Z3, Z2 |
| examples of infinite field | Q |
| finite integral domain that's not a field | impossible |
| infinite integral domain that's not a field | Z |
| a set that is closed under multiplication but not subtraction | N |
| field without unity | impossible |
| ring without unity | 2Z (even integers) |
| polynomial in Q[x], reducible in Q[x] but has no roots in Q | x^4 -4 |
Created by:
monkeyhaha3
Popular Math sets