  An inversive meadow is a commutative ring with identity equipped with a
multiplicative inverse operation made total by choosing 0 as its value at 0.
Previously, inversive meadows were shortly called meadows. A divisive meadow is
an inversive meadows with the multiplicative inverse operation replaced by a
division operation. In the spirit of Peacock's arithmetical algebra, we
introduce variants of inversive and divisive meadows without an additive
identity element and an additive inverse operation. We give equational
axiomatizations of several classes of such variants of inversive and divisive
meadows as well as of several instances of them.

Rings and Algebras;Logic in Computer Science