phitting lemma

ganithashaasthrathil, ganithashaasthranjanaaya hans fittinginte peril ariyappedunna phitting lemma amoortha beejaganithatthile oru adisthaana prasthaavanayaan. m" ennathu eathenkilum valayathinu mukalilulla oru modyoolaanenn karuthuka. m" ennathu nirmmikkaanaavaathathum parimithamaaya neelamullathumaanenkil, "m" yude oro endomorphisavum automorphism allengil nilpottant aanu.
oru pettennulla anantharafalamaayi, oro parimitha-dairkhya indicompossible modyoolinteyum endomorphism ring local aanennu nammal kaanunnu.
grouppukalude praathinidhya sidhaanthathil fittinginte lemmayude oru pathipp palappozhum upayogikkunnu. ithu vaasthavathil mukalilulla pathippinte oru prathyeka kesaanu, kaaranam oru group "jii" yude oro "keey"-leanier praathinidyavum group "kilogram" enna beejaganithatthinte oru modyoolaayi kaanaan kazhiyum.
thelivu.
fittinginte lemma theliyikkaan, nammal "m" nte oru endomorphism "f" edukkukayum submoduleukalude inipparayunna rund shringalakal pariganikkukayum cheiyunnu
formula _ 3 nuu parimithamaaya neelamullathinaal, eee rund shringalakalum oduvil sthiratha kaivarikkanam, athinaal ellah formulakalkkum formula _ 5 ulla chila formula _ 4 undu, koodaathe ellah formulakalkkum formula _ 8 ulla chila formula _ 7 undu.
ippol formula _ 10, nirmmaana formula _ 11, formula _ 12 enniva upayogichu shradhikkuka.
13 enna soothravaakyam nammal avakaashappedunnu. theerchayaayum, oro soothravaakyavum 16 enna soothravaakyathinu 15 enna soothravaakyathe thripthippeduthunnu, mathramalla 17 enna soothravaakyavum, athinaal aaa soothravaakyam 18, athinaal 19 enna soothravaakyam, angane 20 enna soothravaakyam.
koodaathe, formula _ 21: oro formulakkum _ 22, formula _ 24 (formula _ 25 muthal) polulla chila formula _ 16 nilavilundu, angane formula _ 26, angane formula _ 27 umm formula _ 28 umm undu.
thalphalamaayi, formula _ 3 ennathu formula _ 30, formula _ 31 ennivayude nerittulla thukayaanu. (eee prasthavana "phitting decomposition sidhaantham" ennum ariyappedunnu.) formula _ 3 indicompossible aayathinal, aaa rund yogangalil onnu formula _ 3 nuu thulyavum mattonn seero sub module aayirikkanam. rund yogangalil eathaanu poojyamennathine aashrayich, formula _ 34 onnukil bijective allengil nilpottant aanennu nammal kandethunnu.

