Jordan isomorphisms of the finitary incidence ring of a partially ordered category
Let $\mathcal C $ be a pocategory, $FI(\mathcal C )$ the finitary incidence ring of $\mathcal C $, and $\varphi $ a Jordan isomorphism of $FI(\mathcal C )$ onto an associative ring $A$. We study the problem of decomposition of $\varphi $ into the (near-)sum of a homomorphism and an anti-homomorphism. In particular, we obtain generalizations of the main results of Akkurt et al. (2015) and Brusamarello et al. (2018).