J-Boolean group rings and skew group rings

2018 ◽  
Vol 17 (11) ◽  
pp. 1850210
Author(s):  
Dinesh Udar ◽  
R. K. Sharma ◽  
J. B. Srivastava
Keyword(s):  
Jacobson Radical ◽  
Group Rings ◽  
Basic Properties ◽  
Boolean Rings ◽  
Skew Group Rings

A ring [Formula: see text] is called semiboolean if [Formula: see text] is boolean and idempotents lift modulo [Formula: see text], where [Formula: see text] denotes the Jacobson radical of [Formula: see text]. In this paper, we define [Formula: see text]-boolean rings as a generalization of semiboolean rings. A ring [Formula: see text] is said to be J-boolean if [Formula: see text] is boolean. Various basic properties of these rings are obtained. The [Formula: see text]-boolean group rings and skew group rings have been studied. It is investigated whether the results obtained for [Formula: see text]-boolean group rings also hold for the skew group rings.

Outer Partial Actions and Partial Skew Group Rings

2015 ◽  
Vol 67 (5) ◽  
pp. 1144-1160 ◽  
Author(s):  
Patrik Nystedt ◽  
Johan Öinert
Keyword(s):  
Abelian Group ◽  
Dynamical Systems ◽  
Group Ring ◽  
Group Rings ◽  
Partial Action ◽  
Unital Ring ◽  
Different Types ◽  
Outer Action ◽  
Skew Group Rings ◽  
Skew Group Ring

AbstractWe extend the classical notion of an outer action α of a group G on a unital ring A to the case when α is a partial action on ideals, all of which have local units. We show that if α is an outer partial action of an abelian group G, then its associated partial skew group ring A *α G is simple if and only if A is G-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.

scholarly journals Skew group rings and free rings

1990 ◽  
Vol 131 (2) ◽  
pp. 502-512 ◽  
Author(s):  
D.S Passman
Keyword(s):  
Group Rings ◽  
Skew Group Rings

scholarly journals A CLASS OF EXCHANGE RINGS

2008 ◽  
Vol 50 (3) ◽  
pp. 509-522 ◽  
Author(s):  
TSIU-KWEN LEE ◽  
YIQIANG ZHOU
Keyword(s):  
Exchange Ring ◽  
Glasgow Math ◽  
Basic Properties ◽  
Boolean Rings ◽  
Clean Rings ◽  
Exchange Rings

AbstractIt is well known that a ring R is an exchange ring iff, for any a ∈ R, a−e ∈ (a2−a)R for some e2 = e ∈ R iff, for any a ∈ R, a−e ∈ R(a2−a) for some e2 = e ∈ R. The paper is devoted to a study of the rings R satisfying the condition that for each a ∈ R, a−e ∈ (a2−a)R for a unique e2 = e ∈ R. This condition is not left–right symmetric. The uniquely clean rings discussed in (W. K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasgow Math. J. 46 (2004), 227–236) satisfy this condition. These rings are characterized as the semi-boolean rings with a restricted commutativity for idempotents, where a ring R is semi-boolean iff R/J(R) is boolean and idempotents lift modulo J(R) (or equivalently, R is an exchange ring for which any non-zero idempotent is not the sum of two units). Various basic properties of these rings are developed, and a number of illustrative examples are given.

scholarly journals Leavitt Path Algebras as Partial Skew Group Rings

2014 ◽  
Vol 42 (8) ◽  
pp. 3578-3592 ◽  
Author(s):  
Daniel Gonçalves ◽  
Danilo Royer
Keyword(s):  
Group Rings ◽  
Path Algebras ◽  
Skew Group Rings ◽  
Leavitt Path Algebras

scholarly journals p-Γ-Rings

1970 ◽  
Vol 30 ◽  
pp. 1-10
Author(s):  
Md Mahbubur Rashid ◽  
AC Paul
Keyword(s):  
Key Words ◽  
Jacobson Radical ◽  
Subject Classification ◽  
Radical Class ◽  
Basic Properties

The purpose of this paper is to introduce p-Γ-rings and a few of their most basic properties. Then these have been applied to investigate whether the most important properties like commutativty, being radical class and some other characterizations are preserved under our defined p-Γ-rings. Mathematical subject classification-2000: 16N20, 16N99. Key words: Γ -rings, p-rings, Jacobson radical, Radical class, p-Γ -rings. DOI: http://dx.doi.org/10.3329/ganit.v30i0.8497 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 1-10

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