scholarly journals Projective modules over group rings

1971 ◽  
Vol 19 (3) ◽  
pp. 303-314 ◽  
Author(s):  
Pramod K Sharma
Keyword(s):  
Group Rings ◽  
Projective Modules

scholarly journals Adams operations for projective modules over group rings

1997 ◽  
Vol 122 (1) ◽  
pp. 55-71 ◽  
Author(s):  
BERNHARD KÖCK
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Grothendieck Group ◽  
Base Change ◽  
Group Rings ◽  
Projective Modules ◽  
Power Operations ◽  
Definition Of ◽  
A Finite Group ◽  
Twisted Group Ring

Let R be a commutative ring, Γ a finite group acting on R, and let k∈ℕ be invertible in R. Generalizing a definition of Kervaire, we construct an Adams operation ψk on the Grothendieck group and on the higher K-theory of projective modules over the twisted group ring R#Γ. For this, we generalize Atiyah's cyclic power operations and use shuffle products in higher K-theory. For the Grothendieck group, we show that ψk is multiplicative and that it commutes with base change, with the Cartan homomorphism, and with ψl for any other l which is invertible in R.

Ranks of projective modules of group rings

1985 ◽  
Vol 13 (5) ◽  
pp. 1115-1130 ◽  
Author(s):  
Gerald H. Cliff
Keyword(s):  
Group Rings ◽  
Projective Modules

Commutative nil-clean and $\pi$-Regular Group Rings

2019 ◽  
Vol 2019 (3) ◽  
pp. 33-39
Author(s):  
P.V. Danchev
Keyword(s):  
Group Rings ◽  
Regular Group

A note on Lie nilpotent group rings

1992 ◽  
Vol 45 (3) ◽  
pp. 503-506 ◽  
Author(s):  
R.K. Sharma ◽  
Vikas Bist
Keyword(s):  
Nilpotent Group ◽  
Group Algebra ◽  
Group Rings ◽  
Group Of Units

Let KG be the group algebra of a group G over a field K of characteristic p > 0. It is proved that the following statements are equivalent: KG is Lie nilpotent of class ≤ p, KG is strongly Lie nilpotent of class ≤ p and G′ is a central subgroup of order p. Also, if G is nilpotent and G′ is of order pn then KG is strongly Lie nilpotent of class ≤ pn and both U(KG)/ζ(U(KG)) and U(KG)′ are of exponent pn. Here U(KG) is the group of units of KG. As an application it is shown that for all n ≤ p+ 1, γn(L(KG)) = 0 if and only if γn(KG) = 0.

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