-- Basic of Commutaive Algebra
restart
R=ZZ/101[x,y,z]
M=matrix{{x,y,z}}
kernel M
gens oo -- convert the kernel into a matrix 
kernel oo -- problem solved


-- Example
restart 
R=QQ[x,y]
I1=ideal(x^2,x*y)
gens I1
J1=ideal(x^2,y)
J2=ideal(x)
intersect(J1,J2)
intersect(J1,J2) == I1
radical I1 -- embedded components disappear
primaryDecomposition I1


-- Example
restart
R=QQ[x,y]
I=ideal(x^2-x,y^2-y)
netList primaryDecomposition I
J=ideal(x-y)
I:J
netList primaryDecomposition (I:J)
I+J
R/I