Local automorphisms of finitary incidence algebras

Local derivations of finitary incidence algebras

“…In view of ( 3) and ( 6) the right-hand side of (10) is d((α| y x )(x, y)e xy )(x, y) − (d(e x )α| y x )(x, y) − (α| y x d(e y ))(x, y), which is d(α| y x )(x, y) by the same (10), whence (9). Now let d be an R-linear local derivation of F I(P, R).…”

“…Based on an earlier work by Nowicki [19], Nowicki and Nowosad proved in [21,Theorem 3] that each R-linear local derivation of I(P, R) is a derivation, provided that P is a finite preordered set and R is a commutative ring. Alizadeh and Bitarafan improved a particular case of [21,Theorem 3] In this short note, which was inspired by the recent preprint [10] by Courtemanche, Dugas and Herden, we adapt the ideas from [21] to the infinite case using the technique elaborated in [14,16]. More precisely, we show that each R-linear local derivation of the finitary incidence algebra F I(P, R) of an arbitrary poset P over a commutative unital ring R is a derivation, giving thus another partial generalization of [21, Theorem 3].…”