On 2/21/24 15:46, Hill Strong wrote:
I have quite a few places in the FriCAS source code the following
Join(SemiRng, AbelianMonoid)
What would you call this particular algebraic structure?
The name is actually irrelevant. Since it is a Join, it is actually an
unnamed category in FriCAS that is only there for the purpose of listing
the exports (probably you have found it places like this:
https://github.com/fricas/fricas/blob/master/src/algebra/polycat.spad#L21
or this
https://github.com/fricas/fricas/blob/master/src/algebra/matcat.spad#L723
).
It says nothing more than for functionality that is provided by (for
example) RectangularMatrixCategory, it is enough, if the coefficient
domain is a (possibly non-commutative wrt. multiplication) Ring
(possibly without 1).
It looks as if SemiRng would be enough, but seemingly the existence of
the additive neutral element 0 is required.
Of course, FriCAS could introduce a name for this, and perhaps some day
it will, but it seems not necessary now.
I guess, if you are not satisfied with this answer, Waldek will comment
more on this.
Ralf
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