This symbol represents a boolean
unary function. The argument is a ring R.
When evaluated on R, the function returns true if R is a domain
and false otherwise. A domain is a commutative ring without zero divisors.
This is unary boolean function whose argument should be a ring R.
The value is true if and only if the ring is commutative and every nonzero
element has
a multiplicative
inverse.
Commented Mathematical property (CMP):
If is_commutative(G) and for all a in carrier(G)
there is b in carrier(G) such that a*b = identity(G), then is_field(G).
This symbol represents a boolean
binary function. The first argument is a ring R, the second is an element x of R.
When evaluated on R and x, the function returns true if x a zero divisor and
nonzero in R.
Commented Mathematical property (CMP):
An element x of a ring R
is a zero divisor if and only if it
nonzero and there is a nonzero y in R such that x * y = 0 or y * x = 0.