before second test
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| additive identity | a+o=a
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| multiplicative identity | ax=1
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| additive inverse | a+x=o
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| multiplicative inverse | [a][n]=1
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| subring | ring closed under multiplication and subtraction
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| commutative ring | xy=yx
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| unity | multiplicative identity
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| units | ab=ba=1 (a is a unit)
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| zero divisor | R is a commutative ring, a does not equal 0, b does not equal 0, ab=0
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| integral domain | commutative ring but has no zero divisors
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| field | commutative ring with unity in which every non-zero element is a unit
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| factor of a polynomial | something you can factor out with remainder 0
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| root of a polynomial | plug in that number and get 0
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| 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
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| Theorem 8.2 | A field has no zero divisors
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| Theorem 8.5 | Zn is a field iff n is prime
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| 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
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| Theorem 8.8 | All finite domains are fields
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| examples of finite fields | Z5, Z3, Z2
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| examples of infinite field | Q
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| finite integral domain that's not a field | impossible
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| infinite integral domain that's not a field | Z
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| a set that is closed under multiplication but not subtraction | N
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| field without unity | impossible
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| ring without unity | 2Z (even integers)
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| polynomial in Q[x], reducible in Q[x] but has no roots in Q | x^4 -4
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To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
monkeyhaha3
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