[Haskell-cafe] Equivalence of two expressions

I'm not very familiar with algebra and I have a question. Imagine we have ring K. We also have two expressions formed by elements from K and binary operations (+) (*) from K. Can we decide weather these two expressions are equivalent? If there is such an algorithm, where can I find something in Haskell about it? If there is no such algorithm for a ring, maybe there is for a field?