Geodesic
Cohomological triviality of bimodules over Frobenius algebras
Sbornik. Mathematics, Tome 34 (1978) no. 2, pp. 235-241 
F. R. Bobovich. Cohomological triviality of bimodules over Frobenius algebras. Sbornik. Mathematics, Tome 34 (1978) no. 2, pp. 235-241. http://geodesic.mathdoc.fr/item/SM_1978_34_2_a6/
@article{SM_1978_34_2_a6,
     author = {F. R. Bobovich},
     title = {Cohomological triviality of bimodules over {Frobenius} algebras},
     journal = {Sbornik. Mathematics},
     pages = {235--241},
     year = {1978},
     volume = {34},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_2_a6/}
}
TY  - JOUR
AU  - F. R. Bobovich
TI  - Cohomological triviality of bimodules over Frobenius algebras
JO  - Sbornik. Mathematics
PY  - 1978
SP  - 235
EP  - 241
VL  - 34
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1978_34_2_a6/
LA  - en
ID  - SM_1978_34_2_a6
ER  - 
%0 Journal Article
%A F. R. Bobovich
%T Cohomological triviality of bimodules over Frobenius algebras
%J Sbornik. Mathematics
%D 1978
%P 235-241
%V 34
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1978_34_2_a6/
%G en
%F SM_1978_34_2_a6

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

The structure of Frobenius $Z_p$-algebras with disjointness condition is studied. When $p=2$ an analogue of Nakayama's theorem on cohomological triviality is proved for suitable algebras whose radical squared is zero. When $p\ne2$, cohomological triviality in all dimensions will not generally be implied by the vanishing of cohomology in a single dimension, but will follow from the vanishing in two successive dimensions. Bibliography: 9 titles.

[1] F. R. Bobovich, “Proektivnye rezolventy i kogomologicheskaya trivialnost $p$-aperiodicheskikh bimodulei nad frobeniusovymi poryadkami”, Matem. sb., 90(132) (1973), 23–33 | Zbl

[2] Ch. Kertis, I. Rainer, Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, izd-vo “Nauka”, Moskva, 1969 | MR

[3] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, IL, Moskva, 1960

[4] N. Dzhekobson, Stroenie kolets, IL, Moskva, 1961

[5] R. Raghavendran, “Finite associative rings”, Comp. Math., 21:2 (1969), 195–220 | MR

[6] S. Eilenberg, T. Nakayama, “On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings”, Nagoya Math. J., 9 (1955), 1–16 | MR | Zbl

[7] F. R. Bobovich, D. K. Faddeev, “O kogomologiyakh Khokhshilda dlya $Z$-kolets so stepennym bazisom”, Matem. zametki, 4:2 (1968), 141–150 | MR

[8] T. Nakayama, “On modules of trivial cohomology over a finite group. III”, J. Math., 1:1 (1957), 36–46 | MR

[9] H. Ogawa, “On a duality of cohomology groups of Frobenius algebras”, Tǒhoku Math. J., 13:1 (1961), 46–65 | MR | Zbl