A STUDY ON COMMUTATIVITY THEOREMS FOR RINGS AND NEAR-RINGS
A STUDY ON COMMUTATIVITY THEOREMS FOR RINGS AND NEAR-RINGS
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Date
2016-08
Authors
ABDU, MADUGU
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Abstract
This research work deals with commutativity theorems for rings and near-rings with their various generalizations in the setting of some special classes of rings as well as derivations in rings and near-rings. We present their fundamentals and also prove some commutativity results for semi prime rings and ring with unity.We then extended the results to s-unital rings. Some results on commutativity of rings and near-rings are generalized and justified by examples. Posner‟s first theorem isestablished for 𝜎−prime rings. Jordan left and right 𝜎−derivations as well as generalized Jordan left and right 𝜎−derivations on 𝜎−rings are investigated. Further more,distributive near-ring, pseudo-abelian near-ring and distributively generated near-rings are introduced andthese help in developing certain class of derivations on near-rings. Finally, permuting 4−(𝜎,𝜏) derivations on prime near-rings are generalized to permuting 𝑛−(𝜎,𝜏) derivations.
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A THESIS SUBMITTED TO THE DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA IN PARTIAL FULFILMENT FOR THE AWARD OF DOCTOR OF PHILOSOPY IN MATHEMATICS DEPARTMENT OF MATHEMATICS AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA
Keywords
STUDY,, COMMUTATIVITY,, OREMS,, RINGS,, NEAR-RINGS,