Of course, commutative algebra is a fundamental topic in algebraic geometry, number theory, representation theory, and so on.
However, there are some instances (most obviously tropical geometry) where one wishes to consider commutative rigs (or semirings) instead of commutative rings. Although most of the basic concepts of commutative algebra generalize to this setting, it's not as obvious which of commutative algebra's most famous theorems also generalize. And unfortunately there aren't canonical texts along the lines of Atiyah-Macdonald or Eisenbud or Matsumura.
Does anyone know of a good reference for learning commutative algebra over semirings?