Definition
A locally finite poset is one for which every closed interval
- = {x : a ≤ x ≤ b}
within it is finite.
The members of the incidence algebra are the functions f assigning to each nonempty interval a scalar f(a, b), which is taken from the ring of scalars, a commutative ring with unity. On this underlying set one defines addition and scalar multiplication pointwise, and "multiplication" in the incidence algebra is a convolution defined by
An incidence algebra is finite-dimensional if and only if the underlying poset is finite.
Read more about this topic: Incidence Algebra
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