Geodesic
Isomorphisms of groups of invertible elements of incidence algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 257-261 
V. D. Shmatkov. Isomorphisms of groups of invertible elements of incidence algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 257-261. http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a12/
@article{FPM_2016_21_2_a12,
     author = {V. D. Shmatkov},
     title = {Isomorphisms of groups of invertible elements of incidence algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {257--261},
     year = {2016},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a12/}
}
TY  - JOUR
AU  - V. D. Shmatkov
TI  - Isomorphisms of groups of invertible elements of incidence algebras
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2016
SP  - 257
EP  - 261
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a12/
LA  - ru
ID  - FPM_2016_21_2_a12
ER  - 
%0 Journal Article
%A V. D. Shmatkov
%T Isomorphisms of groups of invertible elements of incidence algebras
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2016
%P 257-261
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a12/
%G ru
%F FPM_2016_21_2_a12

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper shows that isomorphisms of groups of invertible elements of incidence algebras imply isomorphisms of the partial orders defining the algebras.

[1] Pomfre Zh., Makdonald B., “Avtomorfizmy gruppy $\mathrm{GL}_{n}$ nad lokalnym koltsom”, Avtomorfizmy klassicheskikh grupp, ed. Yu. I. Merzlyakov, Mir, M., 1976 | MR

[2] Shmatkov V. D., “Izomorfizmy algebr intsidentnosti”, Diskret. matem., 3:1 (1991), 133–144 | MR

[3] Abrams G., Haefner J., del Rio A., “The isomorphism problem for incidence rings”, Pacific J. Math., 187:2 (1999), 201–214 | DOI | MR | Zbl

[4] Spiegel E., O'Donnell C., Incidence Algebras, Chapman Hall/CRC Pure Appl. Math., 206, CRC Press, 1997