Mark each of the following true or false. ___ a. Q is a field of quotients of
Question:
Mark each of the following true or false.
___ a. Q is a field of quotients of Z.
___ b. R is a field of quotients of Z.
___ c. R is a field of quotients of R
___ d. C is a field of quotients of R.
___ e. If D is a field, then any field of quotients of D is isomorphic to D.
___ f. The fact that D has no divisors of 0 was used strongly several times in the construction of a field F of quotients of the integral domain D.
___ g. Every element of an integral domain Dis a unit in a field F of quotients of D.
___ h. Every nonzero element of an integral domain D is a unit in a field F of quotients of D.
___ i. A field of quotients F' of a subdomain D' of an integral domain D can be regarded as a subfield of some field of quotients of D.
___ j. Every field of quotients of Z is isomorphic to Q.
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