▁project ive ▁modules ). ▁Since ▁the ▁algebraic ▁K - theory ▁of ▁a ▁ring ▁is ▁defined ▁( in ▁Qu ill en ' s ▁approach ) ▁in ▁terms ▁of ▁the ▁hom ot opy ▁groups ▁of ▁( rough ly ) ▁the ▁class ifying ▁space ▁of ▁the ▁n erve ▁of ▁the ▁( small ) ▁category ▁of ▁finit ely ▁generated ▁project ive ▁modules ▁over ▁the ▁ring , ▁Mor ita ▁equivalent ▁rings ▁must ▁have ▁is omorphic ▁K - groups . ▁ ▁References ▁ ▁Further ▁reading ▁▁▁ ▁* ▁Module ▁Category : R ing ▁theory ▁Category : Ad joint ▁fun ctors ▁Category : D ual ity ▁theories ▁Category : Equ ival ence ▁( math emat ics ) <0x0A> </s> ▁A ▁common ▁definition ▁of ▁separ at ism ▁is ▁that ▁it ▁is ▁the ▁advoc acy ▁of ▁a ▁state ▁of ▁cultural , ▁eth nic , ▁trib al , ▁religious , ▁ra cial , ▁government al ▁or ▁gender ▁separation ▁from ▁the ▁larger ▁group . ▁While ▁it ▁often ▁refers ▁to ▁full ▁political ▁se cess ion , ▁separ at ist ▁groups ▁may ▁seek ▁nothing ▁more ▁than ▁greater ▁aut onomy . ▁While ▁some ▁critics ▁may ▁equ ate ▁separ at ism ▁with ▁religious ▁seg reg ation , ▁rac ist ▁seg reg ation , ▁or ▁sex ist ▁seg reg ation , ▁most ▁separ at ists ▁argue ▁that ▁separation ▁by ▁choice ▁ ▁may ▁serve ▁useful ▁purposes ▁and ▁is ▁not ▁the ▁same ▁as ▁government - en for ced ▁seg reg ation . ▁There ▁is ▁some ▁academic ▁debate ▁about ▁this ▁definition , ▁and ▁in ▁particular ▁how ▁it ▁rel ates ▁to ▁se cess ion