▁to ▁define ▁a ▁connection ▁on ▁an ▁R - S - b im od ule ▁over ▁non comm ut ative ▁rings ▁R ▁and ▁S . ▁There ▁are ▁different ▁definitions ▁of ▁such ▁a ▁connection . ▁Let ▁us ▁mention ▁one ▁of ▁them . ▁A ▁connection ▁on ▁an ▁R - S - b im od ule ▁ ▁is ▁defined ▁as ▁a ▁b im od ule ▁morph ism ▁▁▁▁ ▁which ▁ob e ys ▁the ▁Le ib n iz ▁rule ▁ ▁See ▁also ▁▁ ▁Connection ▁( vector ▁bundle ) ▁ ▁Connection ▁( math emat ics ) ▁Non comm ut ative ▁geometry ▁Super geometry ▁ ▁D iffer ential ▁calculus ▁over ▁commut ative ▁al gebras ▁ ▁Notes ▁ ▁References ▁▁▁ ▁K osz ul , ▁J ., ▁Hom ologie ▁et ▁coh om ologie ▁des ▁al geb res ▁de ▁Lie , B ul letin ▁de ▁la ▁Soci ete ▁Mathemat ique ▁ 7 8 ▁( 1 9 5 0 ) ▁ 6 5 ▁ ▁K osz ul , ▁J ., ▁L ect ures ▁on ▁F ib re ▁Bund les ▁and ▁D iffer ential ▁Ge ometry ▁( T ata ▁University , ▁Bomb ay , ▁ 1 9 6 0 ) ▁ ▁Bart oc ci , ▁C ., ▁Bru z zo , ▁U ., ▁Hern ande z ▁Ru ip ere z , ▁D ., ▁The ▁Ge ometry ▁of ▁Super man if olds ▁( K lu wer ▁Academ ic ▁Pub l ., ▁ 1 9 9 1 ) ▁▁ ▁Dub ois - V io lette , ▁M ., ▁Mich or , ▁P ., ▁Con ne ctions ▁on