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Automorphisms of finitary incidence rings

Nikolay Khripchenko

Abstract


Let P be a quasiordered set, R an associative unital ring,  C(P,R) a partially ordered category associated with the pair (P,R)[6], FI(P,R) a finitary incidence ring of C(P,R)[6]. We prove that the group OutFI of outer automorphisms of FI(P,R) is isomorphic to the group OutC of outer automorphisms of C(P,R) under the assumption that R is indecomposable. In particular, if R is local, the equivalence classes of P are finite and P=iIPi is the decomposition of P into the disjoint union of the connected components, then OutFI(H1(¯P,C(R)). Here H^1(\overline P,C(R)^*) is the first cohomology group of the order complex of the induced poset \overline P with the values in the multiplicative group of central invertible elements of R. As a consequences, Theorem 2 [9], Theorem 5 [2 ] and Theorem 1.2  [8] are obtained.


Keywords


finitary incidence algebra, partially ordered category,quasiordered set, automorphism

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