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 ∈ R, there exists n ∈ Z⁺ such that b < na. 

___ g. An ordering of a ring R is Archimedian if for each a, b ∈ R such that 0 < a, there exists n ∈ Z⁺ such that b < na. 

___ h. If R is an ordered ring and a ∈ R, then -a cannot be positive. 

___ i. If R is an ordered ring and a ∈ R, then either a or -a is positive. 

___ j. Every ordered ring has an infinite number of elements.