| Title:
|
Skew inverse power series rings over a ring with projective socle (English) |
| Author:
|
Paykan, Kamal |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
389-395 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
skew inverse power series ring |
| Keyword:
|
skew polynomial ring |
| Keyword:
|
annihilator |
| Keyword:
|
projective socle ring |
| Keyword:
|
flat socle ring |
| MSC:
|
16P40 |
| MSC:
|
16S36 |
| MSC:
|
16W60 |
| MSC:
|
16W70 |
| idZBL:
|
Zbl 06738526 |
| idMR:
|
MR3661048 |
| DOI:
|
10.21136/CMJ.2017.0672-15 |
| . |
| Date available:
|
2017-06-01T14:27:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146763 |
| . |
| Reference:
|
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