Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings
Let R be a prime ring with characteristic different from 2 , let U be its right Utumi quotient ring, let C be its extended centroid, let F and G be additive maps on R , let f ( x 1 , . . . ,x n ) be a multilinear polynomial over C , and let I be a nonzero right ideal of R . We obtain information abo...
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| Veröffentlicht in: | Ukrainian mathematical journal 2016-07, Vol.68 (2), p.203-223 |
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| creator | De Filippis, V. Dhara, B. Scudo, G. |
| description | Let
R
be a prime ring with characteristic different from 2
,
let
U
be its right Utumi quotient ring, let
C
be its extended centroid, let
F
and
G
be additive maps on
R
, let
f
(
x
1
, . . . ,x
n
) be a multilinear polynomial over
C
, and let
I
be a nonzero right ideal of
R
. We obtain information about the structure of
R
and describe the form of
F
and
G
in the following cases:
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
R
, where
F
and
G
are generalized derivations of
R
;
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
I
, where
F
and
G
are derivations of
R
. |
| doi_str_mv | 10.1007/s11253-016-1219-0 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_1880847312</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A499343140</galeid><sourcerecordid>A499343140</sourcerecordid><originalsourceid>FETCH-LOGICAL-c377t-b537f2d10de7ed4f89bb3611f1cc399494f0c8fc87dfe5585a8d23309e0a6daa3</originalsourceid><addsrcrecordid>eNp1kE9rGzEQxUVJIE7aD5CboOd1NKtdSzoap3UDMTElORYhr0ZGYVdypHUg_fSR2RxyCXMYeLzf_HmEXAObA2PiJgPULa8YLCqoQVXsG5lBK3iluFickRljDVStUu0Fucz5mbFCSTEj_9YYMJne_0dLbzH5VzP6GDI1wdJVHIbj6MOeLq31o39FujGHTGOgm2M_-t4HNIluY_8W4uBNn6kPdJv8gPRvwfJ3cu6Kij8--hV5-v3rcfWnun9Y362W91XHhRirXcuFqy0wiwJt46Ta7fgCwEHXcaUa1TjWSddJYR22rWyNtDXnTCEzC2sMvyI_p7mHFF-OmEf9HI8plJUapGSyERzq4ppPrr3pUfvg4phMV8ri4LsY0PmiLxuleMOhYQWACehSzDmh04fym0lvGpg-xa6n2HWJXZ9i1yemnphcvGGP6dMpX0Lv7iuFfw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1880847312</pqid></control><display><type>article</type><title>Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings</title><source>SpringerLink Journals</source><creator>De Filippis, V. ; Dhara, B. ; Scudo, G.</creator><creatorcontrib>De Filippis, V. ; Dhara, B. ; Scudo, G.</creatorcontrib><description>Let
R
be a prime ring with characteristic different from 2
,
let
U
be its right Utumi quotient ring, let
C
be its extended centroid, let
F
and
G
be additive maps on
R
, let
f
(
x
1
, . . . ,x
n
) be a multilinear polynomial over
C
, and let
I
be a nonzero right ideal of
R
. We obtain information about the structure of
R
and describe the form of
F
and
G
in the following cases:
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
R
, where
F
and
G
are generalized derivations of
R
;
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
I
, where
F
and
G
are derivations of
R
.</description><identifier>ISSN: 0041-5995</identifier><identifier>EISSN: 1573-9376</identifier><identifier>DOI: 10.1007/s11253-016-1219-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Mathematics ; Mathematics and Statistics ; Polynomials ; Statistics</subject><ispartof>Ukrainian mathematical journal, 2016-07, Vol.68 (2), p.203-223</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>COPYRIGHT 2016 Springer</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c377t-b537f2d10de7ed4f89bb3611f1cc399494f0c8fc87dfe5585a8d23309e0a6daa3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11253-016-1219-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11253-016-1219-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>De Filippis, V.</creatorcontrib><creatorcontrib>Dhara, B.</creatorcontrib><creatorcontrib>Scudo, G.</creatorcontrib><title>Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings</title><title>Ukrainian mathematical journal</title><addtitle>Ukr Math J</addtitle><description>Let
R
be a prime ring with characteristic different from 2
,
let
U
be its right Utumi quotient ring, let
C
be its extended centroid, let
F
and
G
be additive maps on
R
, let
f
(
x
1
, . . . ,x
n
) be a multilinear polynomial over
C
, and let
I
be a nonzero right ideal of
R
. We obtain information about the structure of
R
and describe the form of
F
and
G
in the following cases:
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
R
, where
F
and
G
are generalized derivations of
R
;
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
I
, where
F
and
G
are derivations of
R
.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Statistics</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kE9rGzEQxUVJIE7aD5CboOd1NKtdSzoap3UDMTElORYhr0ZGYVdypHUg_fSR2RxyCXMYeLzf_HmEXAObA2PiJgPULa8YLCqoQVXsG5lBK3iluFickRljDVStUu0Fucz5mbFCSTEj_9YYMJne_0dLbzH5VzP6GDI1wdJVHIbj6MOeLq31o39FujGHTGOgm2M_-t4HNIluY_8W4uBNn6kPdJv8gPRvwfJ3cu6Kij8--hV5-v3rcfWnun9Y362W91XHhRirXcuFqy0wiwJt46Ta7fgCwEHXcaUa1TjWSddJYR22rWyNtDXnTCEzC2sMvyI_p7mHFF-OmEf9HI8plJUapGSyERzq4ppPrr3pUfvg4phMV8ri4LsY0PmiLxuleMOhYQWACehSzDmh04fym0lvGpg-xa6n2HWJXZ9i1yemnphcvGGP6dMpX0Lv7iuFfw</recordid><startdate>20160701</startdate><enddate>20160701</enddate><creator>De Filippis, V.</creator><creator>Dhara, B.</creator><creator>Scudo, G.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160701</creationdate><title>Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings</title><author>De Filippis, V. ; Dhara, B. ; Scudo, G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c377t-b537f2d10de7ed4f89bb3611f1cc399494f0c8fc87dfe5585a8d23309e0a6daa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>De Filippis, V.</creatorcontrib><creatorcontrib>Dhara, B.</creatorcontrib><creatorcontrib>Scudo, G.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>De Filippis, V.</au><au>Dhara, B.</au><au>Scudo, G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2016-07-01</date><risdate>2016</risdate><volume>68</volume><issue>2</issue><spage>203</spage><epage>223</epage><pages>203-223</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>Let
R
be a prime ring with characteristic different from 2
,
let
U
be its right Utumi quotient ring, let
C
be its extended centroid, let
F
and
G
be additive maps on
R
, let
f
(
x
1
, . . . ,x
n
) be a multilinear polynomial over
C
, and let
I
be a nonzero right ideal of
R
. We obtain information about the structure of
R
and describe the form of
F
and
G
in the following cases:
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
R
, where
F
and
G
are generalized derivations of
R
;
[(
F
2
+
G
)(
f
(
r
1
, . . . , r
n
))
, f
(
r
1
, . . . , r
n
)] = 0 for all
r
1
, . . . , r
n
∈
I
, where
F
and
G
are derivations of
R
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11253-016-1219-0</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2016-07, Vol.68 (2), p.203-223 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_proquest_journals_1880847312 |
| source | SpringerLink Journals |
| subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Polynomials Statistics |
| title | Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings |
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