منابع مشابه
On Regular Group Rings
Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...
متن کاملInvertibility of Finite Group Homomorphic Sequential Systems
T h e question of invertibil i ty of a dynamical system-i .e . , when does the output sequence (function) uniquely determine the input sequence ( funct ion)--has received a good deal of attention in the literature and has applications to problems in coding theory and functional controllabili ty (the dual of invertibility). Massey and Sain (1968), Sain and Massey (1969), Brockett and Mesarovic (...
متن کاملCOTORSION DIMENSIONS OVER GROUP RINGS
Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.
متن کاملNormality in Group Rings
Let KG be the group ring of a group G over a commutative ring K with unity. The rings KG are described for which xxσ = xσx for all x = ∑ g∈G αgg ∈ KG, where x → xσ = ∑ g∈G αgf(g)σ(g) is an involution of KG; here f : G → U(K) is a homomorphism and σ is an antiautomorphism of order two of G. Let R be a ring with unity. We denote by U(R) the group of units of R. A (bijective) map : R → R is called...
متن کاملGroup rings satisfying generalized Engel conditions
Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1) y]=[[x ,_( n) y] , y]. In this paper we show that necessary and sufficient conditions for RG to satisfies [x^m(x,y) ,_( n(x,y)) y]=0 is: 1) if r is a power of a prime p, then G is a locally nilpotent group an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2019
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1919141m