Prime Ideals in Polycyclic Group Rings

2009 ◽  
pp. 89-98
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Polycyclic Group ◽  
Prime Ideals ◽  
Group Rings

The structure of modules over polycyclic groups

1981 ◽  
Vol 89 (2) ◽  
pp. 257-283 ◽  
Author(s):  
Kenneth A. Brown
Keyword(s):  
Representation Theory ◽  
Polynomial Identity ◽  
Polycyclic Group ◽  
Prime Ideals ◽  
Group Rings ◽  
Polycyclic Groups

AbstractThe structure of modules over polycyclic group rings RG is investigated using the idea of a link P ⇝ Q between prime ideals of RG. The representation theory of RG splits into two parts – the part we discuss is determined by the representation theory of certain Noetherian polynomial identity factor rings of subrings of RG.

scholarly journals Group rings which are v-HC orders and Krull orders

1991 ◽  
Vol 34 (2) ◽  
pp. 217-228 ◽  
Author(s):  
K. A. Brown ◽  
H. Marubayashi ◽  
P. F. Smith
Keyword(s):  
Finite Group ◽  
Group Ring ◽  
Prime Ideals ◽  
Group Rings

Let R be a ring and G a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and G, when the group ring R[G] is a prime Krull order and when it is a price v-HC order. The key ingredient in obtaining both characterizations is the first author's earlier study of height one prime ideals in the ring R[G[.

scholarly journals Prime ideals and localization in commutative group rings

1975 ◽  
Vol 34 (2) ◽  
pp. 300-308 ◽  
Author(s):  
J.W Brewer ◽  
D.L Costa ◽  
E.L Lady
Keyword(s):  
Commutative Group ◽  
Prime Ideals ◽  
Group Rings

Ore Extensions and Polycyclic Group Rings

1974 ◽  
Vol s2-9 (2) ◽  
pp. 337-345 ◽  
Author(s):  
Alfred Goldie ◽  
Gerhard Michler
Keyword(s):  
Polycyclic Group ◽  
Group Rings ◽  
Ore Extensions

Trace Functions in the Ring of Fractions of Polycyclic Group Rings, II

1997 ◽  
Vol 49 (4) ◽  
pp. 788-797
Author(s):  
A. I. Lichtman
Keyword(s):  
Finite Group ◽  
Polycyclic Group ◽  
Trace Function ◽  
Group Rings ◽  
Ring Of Fractions

AbstractWe prove the existence of trace functions in the rings of fractions of polycyclic-by-finite group rings or their homomorphic images. In particular a trace function exists in the ring of fractions of KH, where H is a polycyclic-by-finite group and char K > N, where N is a constant depending on H.

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