2024/01/31 by Kaigorodov, Evgenii, Krylov, Piotr, Tuganbaev, Askar
#16S50 #16W20 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2401.17964
Let I(X,R) be the incidence algebra of the preordered set X over the ring R. In the case of a finite connected partially ordered set X, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra I(X,R). As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms.