Geodesic
Skew inverse power series rings over a ring with projective socle
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 389-395

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A ring $R$ is called a right $\rm PS$-ring if its socle, ${\rm Soc}(R_{R} )$, is projective. Nicholson and Watters have shown that if $R$ is a right $\rm PS$-ring, then so are the polynomial ring $R[x]$ and power series ring $R[[x]]$. In this paper, it is proved that, under suitable conditions, if $R$ has a (flat) projective socle, then so does the skew inverse power series ring $R[[x^{-1};\alpha , \delta ]]$ and the skew polynomial ring $R[x;\alpha , \delta ]$, where $R$ is an associative ring equipped with an automorphism $\alpha $ and an $\alpha $-derivation $\delta $. Our results extend and unify many existing results. Examples to illustrate and delimit the theory are provided.
DOI : 10.21136/CMJ.2017.0672-15
Classification : 16P40, 16S36, 16W60, 16W70
Keywords: skew inverse power series ring; skew polynomial ring; annihilator; projective socle ring; flat socle ring 
@article{10_21136_CMJ_2017_0672_15,
     author = {Paykan, Kamal},
     title = {Skew inverse power series rings over a ring with projective socle},
     journal = {Czechoslovak Mathematical Journal},
     pages = {389--395},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2017},
     doi = {10.21136/CMJ.2017.0672-15},
     mrnumber = {3661048},
     zbl = {06738526},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0672-15/}
}
TY  - JOUR
AU  - Paykan, Kamal
TI  - Skew inverse power series rings over a ring with projective socle
JO  - Czechoslovak Mathematical Journal
PY  - 2017
SP  - 389
EP  - 395
VL  - 67
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0672-15/
DO  - 10.21136/CMJ.2017.0672-15
LA  - en
ID  - 10_21136_CMJ_2017_0672_15
ER  - 
%0 Journal Article
%A Paykan, Kamal
%T Skew inverse power series rings over a ring with projective socle
%J Czechoslovak Mathematical Journal
%D 2017
%P 389-395
%V 67
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0672-15/
%R 10.21136/CMJ.2017.0672-15
%G en
%F 10_21136_CMJ_2017_0672_15
Paykan, Kamal. Skew inverse power series rings over a ring with projective socle. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 389-395. doi: 10.21136/CMJ.2017.0672-15

Cité par Sources :