In this paper, it is defined that left style="font-family:Verdana;">*- style="font-family:Verdana;">α style="font-family:Verdana;">-derivation, generalized left style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">- style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;">-derivation and style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">- style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;">-derivation, generalized style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">- style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;">-derivation of a style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">-ring where style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;"> is a homomorphism. The results which proved for generalized left style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">-derivation of style="font-family:Verdana;font-size:12px;">R style="font-family:Verdana;font-size:12px;"> in times="" new="" roman","serif";"="" style="font-size: 10pt;"> style="font-family:Verdana;font-size:12px;"> style="font-family:Verdana;">[1] minion="" pro="" capt","serif";color:#943634;"="" style="font-size: 10pt;"> style="font-size:10pt;font-family:;" "=""> times="" new="" roman","serif";"="" style="font-size: 10pt;"> style="font-family:Verdana;"> are extended by using generalized left style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">- style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;">-derivation. The commutativity of a style="font-family:Verdana;">* style="font-family:Verdana;">-ring with generalized left style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">- style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;">-derivation is investigated and some results are given for generalized style="font-family:Verdana;">* style="font-size:10pt;font-family:;" "=""> style="font-family:Verdana;font-size:12px;">- style="font-family:Verdana;font-size:12px;">α style="font-family:Verdana;font-size:12px;">-derivation.
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