Power values of quadratic polynomials with generalized skew derivations on Lie ideals
Let R be a prime ring of characteristic different from 2, Z ( R ) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R , L a non-central Lie ideal of R and n ≥ 1 a fixed integer such that [ F ( x ) , y ] n = [ x , F ( y ) ] n , for all x , y...
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| Veröffentlicht in: | Beiträge zur Algebra und Geometrie 2021-12, Vol.62 (4), p.893-905 |
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| container_title | Beiträge zur Algebra und Geometrie |
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| creator | Ali, Asma De Filippis, Vincenzo |
| description | Let
R
be a prime ring of characteristic different from 2,
Z
(
R
) its center,
Q
its right Martindale quotient ring,
C
its extended centroid,
F
a generalized skew derivation of
R
,
L
a non-central Lie ideal of
R
and
n
≥
1
a fixed integer such that
[
F
(
x
)
,
y
]
n
=
[
x
,
F
(
y
)
]
n
, for all
x
,
y
∈
L
. Then there exists
λ
∈
C
such that
F
(
x
)
=
λ
x
, for any
x
∈
R
, unless
R
is an order in a 4-dimensional central simple algebra. |
| doi_str_mv | 10.1007/s13366-020-00550-3 |
| format | Article |
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R
be a prime ring of characteristic different from 2,
Z
(
R
) its center,
Q
its right Martindale quotient ring,
C
its extended centroid,
F
a generalized skew derivation of
R
,
L
a non-central Lie ideal of
R
and
n
≥
1
a fixed integer such that
[
F
(
x
)
,
y
]
n
=
[
x
,
F
(
y
)
]
n
, for all
x
,
y
∈
L
. Then there exists
λ
∈
C
such that
F
(
x
)
=
λ
x
, for any
x
∈
R
, unless
R
is an order in a 4-dimensional central simple algebra.</description><identifier>ISSN: 0138-4821</identifier><identifier>EISSN: 2191-0383</identifier><identifier>DOI: 10.1007/s13366-020-00550-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Algebraic Geometry ; Centroids ; Convex and Discrete Geometry ; Geometry ; Mathematics ; Mathematics and Statistics ; Original Paper ; Polynomials ; Quotients</subject><ispartof>Beiträge zur Algebra und Geometrie, 2021-12, Vol.62 (4), p.893-905</ispartof><rights>The Managing Editors 2021</rights><rights>The Managing Editors 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-329b4e70b9d262ece0511577498bcb65838a3969b7ad4721ec2bfe8dde18cbf93</cites><orcidid>0000-0002-3213-1254</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13366-020-00550-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13366-020-00550-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Ali, Asma</creatorcontrib><creatorcontrib>De Filippis, Vincenzo</creatorcontrib><title>Power values of quadratic polynomials with generalized skew derivations on Lie ideals</title><title>Beiträge zur Algebra und Geometrie</title><addtitle>Beitr Algebra Geom</addtitle><description>Let
R
be a prime ring of characteristic different from 2,
Z
(
R
) its center,
Q
its right Martindale quotient ring,
C
its extended centroid,
F
a generalized skew derivation of
R
,
L
a non-central Lie ideal of
R
and
n
≥
1
a fixed integer such that
[
F
(
x
)
,
y
]
n
=
[
x
,
F
(
y
)
]
n
, for all
x
,
y
∈
L
. Then there exists
λ
∈
C
such that
F
(
x
)
=
λ
x
, for any
x
∈
R
, unless
R
is an order in a 4-dimensional central simple algebra.</description><subject>Algebra</subject><subject>Algebraic Geometry</subject><subject>Centroids</subject><subject>Convex and Discrete Geometry</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Polynomials</subject><subject>Quotients</subject><issn>0138-4821</issn><issn>2191-0383</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEuXxA6wssQ6M7Th2lqjiJVWCBV1bSTwpLmnc2mmr8vUYgsSO1d2ce0dzCLlicMMA1G1kQhRFBhwyACkhE0dkwlnJMhBaHJMJMKGzXHN2Ss5iXAJAoZSakPmr32Ogu6rbYqS-pZttZUM1uIaufXfo_cpVXaR7N7zTBfYYqs59oqXxA_fUYnC7xPo-VXs6c0idxcRfkJM2BV7-5jmZP9y_TZ-y2cvj8_RuljVcwZAJXtY5KqhLywuODYJkTCqVl7pu6kJqoStRFmWtKpsrzrDhdYvaWmS6qdtSnJPrcXcd_CY9MJil34Y-nTRclsCkliATxUeqCT7GgK1ZB7eqwsEwMN_6zKjPJH3mR58RqSTGUkxwv8DwN_1P6wtXH3Nq</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Ali, Asma</creator><creator>De Filippis, Vincenzo</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3213-1254</orcidid></search><sort><creationdate>20211201</creationdate><title>Power values of quadratic polynomials with generalized skew derivations on Lie ideals</title><author>Ali, Asma ; De Filippis, Vincenzo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-329b4e70b9d262ece0511577498bcb65838a3969b7ad4721ec2bfe8dde18cbf93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Algebraic Geometry</topic><topic>Centroids</topic><topic>Convex and Discrete Geometry</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Polynomials</topic><topic>Quotients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ali, Asma</creatorcontrib><creatorcontrib>De Filippis, Vincenzo</creatorcontrib><collection>CrossRef</collection><jtitle>Beiträge zur Algebra und Geometrie</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ali, Asma</au><au>De Filippis, Vincenzo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Power values of quadratic polynomials with generalized skew derivations on Lie ideals</atitle><jtitle>Beiträge zur Algebra und Geometrie</jtitle><stitle>Beitr Algebra Geom</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>62</volume><issue>4</issue><spage>893</spage><epage>905</epage><pages>893-905</pages><issn>0138-4821</issn><eissn>2191-0383</eissn><abstract>Let
R
be a prime ring of characteristic different from 2,
Z
(
R
) its center,
Q
its right Martindale quotient ring,
C
its extended centroid,
F
a generalized skew derivation of
R
,
L
a non-central Lie ideal of
R
and
n
≥
1
a fixed integer such that
[
F
(
x
)
,
y
]
n
=
[
x
,
F
(
y
)
]
n
, for all
x
,
y
∈
L
. Then there exists
λ
∈
C
such that
F
(
x
)
=
λ
x
, for any
x
∈
R
, unless
R
is an order in a 4-dimensional central simple algebra.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s13366-020-00550-3</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0002-3213-1254</orcidid></addata></record> |
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| identifier | ISSN: 0138-4821 |
| ispartof | Beiträge zur Algebra und Geometrie, 2021-12, Vol.62 (4), p.893-905 |
| issn | 0138-4821 2191-0383 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Algebraic Geometry Centroids Convex and Discrete Geometry Geometry Mathematics Mathematics and Statistics Original Paper Polynomials Quotients |
| title | Power values of quadratic polynomials with generalized skew derivations on Lie ideals |
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