Is the zero ring a domain? Is the zero ring usually considered a domain or not? Wikipedia says:

  
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*The zero ring is not an integral domain; this agrees with the fact that its zero ideal is not prime. Whether the zero ring is considered to be a domain at all is a matter of convention, but there are two advantages to considering it not to be a domain. First, this agrees with the definition that a domain is a ring in which $0$ is the only zero divisor (in particular, $0$ is required to be a zero divisor, which fails in the zero ring). Second, this way, for a positive integer $n$, the ring $\Bbb Z/n\Bbb Z$ is a domain if and only if n is prime.
  

What are the arguments for/against this convention (besides the ones listed above)? What does the literature (i.e. your favorite textbooks) say on this matter? Note that I am specifically talking about domains, not integral domains; the only difference between them aside from the non-triviality assumption mentioned here is that domains are not required to be commutative.
 A: I would like domains to have fields of fractions. Fractions are equivalence classes of ordered pairs $(p,q)$ where $q \neq 0$. Since all elements of the zero ring are zero, there are no such pairs and one deduces that the "field of fractions" should be the empty set. But the empty set is not a field (does not contain $0$ or $1$.)
A: 
Is the zero ring usually considered a domain or not?

Nearly every ring theory text says it is not. I bet guessing that 90% of texts agree with this is a conservative guess.
The main thing is what the first sentence you cited tries to say (but does not do a good job with): we want to say that $R/P$ is a prime ring if and only if $P$ is a prime ideal. (For noncommutative rings, this becomes $R/P$ is a domain if and only if $P$ is a completely prime ideal, that is, one satisfying the commutative definition of "prime." This does not matter much for the following discussion.)

What does the literature (i.e. your favorite textbooks) say on this matter? 

If $\{0\}$ were considered a domain, then $R/R$ would be a domain for any ring $R$, so that $R$ is a prime ideal of itself. This is (in every reference I know) explicitly ruled out by the definition of a prime ideal. You could of course object that this is just an equivalent question ("why shouldn't the whole ring be considered a prime ideal?") 
A very similar discussion took place here where someone asked why the zero ring wasn't considered a field. The argument that I gave there applies pretty well in this situation too. Our intuition of primes being "indecomposable" leads us to the idea that a prime ring shouldn't decompose into other rings. Certainly decomposing a prime ring into a product of multiple prime rings would be unattractive. But if you let $R=\{0\}$ be a prime ring, then $R\cong\prod_{i\in I} R$ or any nonempty index set that you like.
In particular if we let $\{0\}$ be called a domain, then we'd have a domain that is isomorphic to infinitely many copies of itself, which certainly seems like poor behavior for a domain.
