On automorphisms and derivations of reduced incidence algebras and coalgebras

Incidence algebras of partially ordered sets over commutative rings are an important and characteristic example of function rings. From a partially ordered set, one can obtain an incidence coalgebra. Using certain equivalence relations on the set of all intervals of a locally finite poset, reduced incidence algebras and reduced incidence coalgebras are defined. These objects have a much more complex structure compared to incidence algebras and incidence coalgebras.
This article introduces two types of automorphisms of the reduced incidence algebra -multiplicative and order, as well as one type of derivations - additive derivation. As for incidence coalgebras, there are no works devoted to their automorphisms or derivations. The article discusses a possible approach to the study of automorphisms and derivations of incidence coalgebras.