The structure of finite meadows

• Commutative rings with total inverse operator satisfying 0−1=00−1=0.
• The class of finite meadows is the closure of the class of Galois fields under finite products.
• Unique representation of minimal finite meadows in terms of finite prime fields.

A meadow   is a commutative ring with a total inverse operator satisfying 0−1=00−1=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products. As a corollary, we obtain a unique representation of minimal finite meadows in terms of finite prime fields.