| Meadows (2008) | |||||||||||||||
Abstract | |||||||||||||||
| A meadow is a commutative ring with an inverse operator satisfying two equations and in which 0 −1 = 0. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms for inverse, we start the development of a theory of meadows. We give a general representation theorem for meadows and find, as a corollary, that the equational theory of meadows coincides with the equational theory of zero totalized fields. We also prove representation results for meadows of finite characteristic. 1 | |||||||||||||||
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