It is well known that K<sub>0</sub>R（?）Z（?）（?）<sub>0</sub>R, where R is a commutative ring. So the Grothendieck group of R can be given by the reduced group （?）<sub>0</sub>R...It is well known that K<sub>0</sub>R（?）Z（?）（?）<sub>0</sub>R, where R is a commutative ring. So the Grothendieck group of R can be given by the reduced group （?）<sub>0</sub>R. On the other hand, linear representations of groups can be seen as the finitely generated projective modules over group rings. Thus, it is very useful to study the properties of reduced groups of group rings.展开更多
文摘It is well known that K<sub>0</sub>R（?）Z（?）（?）<sub>0</sub>R, where R is a commutative ring. So the Grothendieck group of R can be given by the reduced group （?）<sub>0</sub>R. On the other hand, linear representations of groups can be seen as the finitely generated projective modules over group rings. Thus, it is very useful to study the properties of reduced groups of group rings.
