Mark each of the following true or false.
_______a. There is only one ordering possible for the ring ℤ.
_______b. The field ℝ can be ordered in only one way.
_______c. Any subfield of ℝ can be ordered in only one way.
_______d. The field ℚ can be ordered in only one way.
_______e. If R is an ordered ring, then R[x] can be ordered in a way that induces the given order on R.
_______f. An ordering of a ring R is Archimedian if for each a, b ϵ R, there exists n ϵ ℤ+ such that b
_______g. An ordering of a ring R is Archimedian if for each a,b ϵ R such that 0 ϵ a, there exists n ϵ ℤ+ such that b
_______h. If R is an ordered ring and a ϵ R, then —a cannot be positive.
_______i. If R is an ordered ring and a ϵ R, then cither a or —a is positive.
_______j. Every ordered ring has an infinite number of elements.
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