Geodesic
On unit group of a finite local rings with 4-nilpotent radical of Jacobson
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 552-567.

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

We describe the structure of the unit group of a commutative finite local rings $R$ of characteristic $p$ with Jacobson radical $J$ such that ${\dim_F J/J^2=2}$, ${\dim_F J^2/J^3=2}$, ${\dim_F J^3=1}$, $J^4=(0)$ and $F=R/J\cong GF(p^r)$, the finite field of $p^r$ elements.
Keywords: local rings, finite rings, unit group of a ring. 
@article{SEMR_2017_14_a15,
     author = {E. V. Zhuravlev},
     title = {On unit group of a finite local rings with 4-nilpotent radical of {Jacobson}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {552--567},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a15/}
}
TY  - JOUR
AU  - E. V. Zhuravlev
TI  - On unit group of a finite local rings with 4-nilpotent radical of Jacobson
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 552
EP  - 567
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a15/
LA  - ru
ID  - SEMR_2017_14_a15
ER  - 
%0 Journal Article
%A E. V. Zhuravlev
%T On unit group of a finite local rings with 4-nilpotent radical of Jacobson
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 552-567
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a15/
%G ru
%F SEMR_2017_14_a15
E. V. Zhuravlev. On unit group of a finite local rings with 4-nilpotent radical of Jacobson. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 552-567. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a15/

[1] R. Raghavendran, “Finite associative rings”, Compositio Math., 21 (1969), 195–229 | MR | Zbl

[2] B.R. McDonald, Finite rings with identity, Decker, 1974 | MR

[3] C.J. Chikunji, “Unit groups of cube radical zero commutative completely primary finite rings”, Int. J. Math. Sci., 4 (2005), 572–579 | MR

[4] C.J. Chikunji, “Unit groups of a certain class of completely primary finite rings”, Math. J. Okayama Univ., 47 (2005), 39–53 | MR | Zbl

[5] R.W. Gilmer, “Finite rings having a cyclic multiplicative group of units”, Amer. J. Math., 85 (1963), 447–452 | DOI | MR | Zbl

[6] G. Ganske, B.R. McDonald, “Finite local rings”, Rocky Mountain J. Math., 3:4 (1973), 521–540 | DOI | MR | Zbl

[7] C.J. Chikunji, “On unit groups of completely primary finite rings”, Math. J. Okayama Univ., 50 (2008), 149–160 | MR | Zbl

[8] C.J. Chikunji, “Unit groups of finite rings with products of zero divisors in their coefficient subrings”, Publication de l'institut mathe'matique, 95(109) (2014), 215–220 | DOI | MR | Zbl

[9] C.J. Chikunji, “Groups of units of commutative completely primary finite rings”, IMHOTEP — Math. Proc., 1 (2014), 40–48 | MR

[10] O.M. Oduor, O.M. Onyango, “Unit groups of some classes of power four radical zero commutative completely primary finite rings”, International Journal of algebra, 8 (2014), 357–363 | DOI

[11] E.V. Zhuravlev, “On unit group of a finite local rings of characteristic $p$”, Siberian Electronic Mathematical Reports, 11 (2014), 362–371 | MR | Zbl

[12] E.V. Zhuravlev, “Local rings of order $p^6$ with 4-nilpotent radical of Jacobson”, Siberian Electronic Mathematical Reports, 3 (2006), 15–29 | MR

[13] E.V. Zhuravlev, “On the classification of finite commutative local rings”, Siberian Electronic Mathematical Reports, 12 (2015), 625–638 | MR | Zbl