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isDomain -- whether a ring is a domain

Description

This function returns true if R is an integral domain, otherwise it returns false. It simply checks whether the zero ideal is prime.

i1 : R = QQ[x,y,z]/ideal(x^2-y*z)

o1 = R

o1 : QuotientRing
 
i2 : isDomain(R)

o2 = true
 
i3 : S = ZZ/5[x,y]/ideal(x^2*y^3)

o3 = S

o3 : QuotientRing
 
i4 : isDomain(S)

o4 = false

Ways to use isDomain:

  • isDomain(Ring)

For the programmer

The object isDomain is a method function.

The source of this document is in WeilDivisors.m2:3306:0.