Generalized strong commutativity preserving centralizers of semiprime rings

Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of R. An additive mappings are called right centralizer if ( ) ( ) and ( ) ( ) holds for all . In the present paper, we introduce the concepts of generalized strong commutativity centralizers preserving and generalized strong cocomm...

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Bibliographic Details
Published in:Iraqi journal of science 2016, Vol.57 (3B), p.2079-2088
Main Authors: Abd al-Jalil, Amirah Amir, Majid, Abd al-Rahman Hamid
Format: Article
Language:ara ; eng
Subjects:
الأعداد الأولية
التفاضل والتكامل الكسري
الحلقات
Online Access:Get full text
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Summary:Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of R. An additive mappings are called right centralizer if ( ) ( ) and ( ) ( ) holds for all . In the present paper, we introduce the concepts of generalized strong commutativity centralizers preserving and generalized strong cocommutativity preserving centralizers and we prove that R contains a nonzero central ideal if any one of the following conditions holds: (i) ( ) ( ), (ii) [ ( ) ( )] , (iii) [ ( ) ( )] [ ], (iv) ( ) ( ) , (v) ( ) ( ) , (vi) [ ( ) ( )] , (vii) ( ) ( ) ( ),
ISSN:0067-2904
2312-1637