agda / agda-stdlib

The Agda standard library

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Refactor `(Is)Nearring` (long-term placeholder)

jamesmckinna opened this issue · comments

Issue #2195 / PR #2209 expose an inadvertent symmetrisation arising from the direct dependency on (Is)Quasiring, namely that the same construction of zero is definable in these structures as well. But while this is not per se in conflict with the Wikipedia definition of left- and right- near-ring, it perhaps suggests our Algebra hierarchy should be a bit more subtle in the distinctions it makes between left- and right- near-rings (and, if need be, all the Algebra.Consequences arising from when the structure is, in fact, fully symmetric wrt left- and right-distributivity etc.). At some point in the future...