Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications

2008 ◽  
Keyword(s):  
Group Rings ◽  
Noncommutative Rings ◽  
Diagram Algebras

Lie centrally metabelian group rings over noncommutative rings

2019 ◽  
Vol 47 (11) ◽  
pp. 4729-4739
Author(s):  
Meena Sahai ◽  
Sheere Farhat Ansari
Keyword(s):  
Metabelian Group ◽  
Group Rings ◽  
Noncommutative Rings

On group modules

2019 ◽  
Vol 19 (07) ◽  
pp. 2050130
Author(s):  
M. Tamer Koşan ◽  
Jan Žemlička
Keyword(s):  
Group Rings ◽  
Noncommutative Rings ◽  
Chain Conditions ◽  
Group Module

The paper is focused on questions when some homological and submodule-chain conditions satisfied by a module [Formula: see text] are preserved by the group module [Formula: see text]. Namely, it is proved for a group [Formula: see text] and an [Formula: see text]-module [Formula: see text] that [Formula: see text] is flat if and only if [Formula: see text] is flat, and [Formula: see text] is artinian if and only if [Formula: see text] is artinian and [Formula: see text] is finite, which are two questions raised by Yiqiang Zhou: On Modules Over Group Rings, Noncommutative Rings and Their Applications LENS July 1-4, 2013.

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.

Subgroups induced by certain ideals of free group rings

1983 ◽  
Vol 11 (22) ◽  
pp. 2519-2525 ◽  
Author(s):  
Chander Kanta Gupta
Keyword(s):  
Free Group ◽  
Group Rings

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

scholarly journals Gauss Units in Integral Group Rings

1998 ◽  
Vol 204 (2) ◽  
pp. 588-596 ◽  
Author(s):  
Olaf Neisse ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings
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