Thanks to a reference provided by Rod McGuire in another thread (here):
we can settle the question of origin of the terminology ’rig’ – because Lawvere writes there, about his work with Schanuel, that:
We were amused when we finally revealed to each other that we had each independently come up with the term ’rig’.
Have added this to the entry.
]]>Thanks, I have added that to the entry.
]]>It appears earlier than 1992, e.g., in
See here, page 379. But I wouldn’t bet this is the earliest appearance either.
]]>added pointer to
Is this (on p. 2) maybe the actual origin of the term “rig”?
]]>Added a reference to Rig
]]>adding paragraph on the relationship between rigs and semirings.
Anonymous
]]>*define a ring to be a monoid object in the category of abelian groups
]]>I’ve seen four different definitions of a “semiring” out there, depending on the author:
The problem is already there in the definition of a ring, as some authors define a ring to be a semigroup object in the category of abelian groups, while other authors define a ring to be a monoid object in the category of commutative monoids
]]>Thank you, it seems very logical to me now. I will use the term rig for the structure with the two identities from now on.
]]>The same is true of Kazimierz Glazek’s A guide to the literature on semirings and their applications in mathematics and information sciences
]]>Semirings as defined on Wolfram MathWorld don’t have either an additive or multiplicative identity; they are semigroup objects in the category of commutative semigroups.
]]>Added link to “multiplicatively cancellable semi-ring”.
]]>