Geodesic
Conjugation properties in incidence algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 111-123.

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Incidence algebras can be regarded as a generalization of full matrix algebras. We present some conjugation properties for incidence functions. The list of results is as follows: a criterion for a convex-diagonal function $f$ to be conjugated to the diagonal function $fe$; conditions under which the conjugacy $f\sim Ce+\zeta_{\lessdot}$ holds (the function $Ce+\zeta_{\lessdot}$ may be thought of as an analog for a Jordan box from matrix theory); a proof of the conjugation of two functions $\zeta_$ and $\zeta_{\lessdot}$ for partially ordered sets that satisfy the conditions mentioned above; an example of a partially ordered set for which the conjugacy $\zeta_\sim \zeta_{\lessdot}$ does not hold. These results involve conjugation criteria for convex-diagonal functions of some partially ordered sets. 
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V. E. Marenich. Conjugation properties in incidence algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 111-123. http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a7/

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