associated prime

naturemath

What is the difference between an associated prime and an embedded prime?

Consider C[x,y]/<x², xy>.

The primary decomposition of < x², xy > is <x> [itex]\cap[/itex] <x,y>², and is this also an associate & an embedded prime?


What is the geometry behind Z(<x², xy>) in C²?


One last question: if a curve or a surface is intersecting itself, is this curve or surface called embedded curve/surface?