Morphic group rings
نویسندگان
چکیده
منابع مشابه
Generalizations of Morphic Group Rings
An element a in a ring R is called left morphic if there exists b ∈ R such that 1R(a)= Rb and 1R(b)= Ra. R is called left morphic if every element ofR is left morphic. An element a in a ring R is called left π-morphic (resp., left G-morphic) if there exists a positive integer n such that an (resp., an with an = 0) is left morphic. R is called left π-morphic (resp., left G-morphic) if every elem...
متن کاملMorphic and Principal-ideal Group Rings
We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For R an artinian principal ideal ring and G a group, we characterize when RG is a principal ideal ring; for finite groups G, this characterizes when RG is a left and right morphic ring. This extends work of Passman, Sehgal and Fisher in the case when R is a...
متن کاملGeneralized Morphic Rings and Their Applications
Let R be a ring. An element a in R is called left morphic (Nicholson and Sánchez Campos, 2004a) if l a R/Ra, where l a denotes the left annihilator of a in R. The ring itself is called a left morphic ring if every element is left morphic. Left morphic rings were first introduced by Nicholson and Sánchez Campos (2004a) and were discussed in great detail there and in Nicholson and Sánchez Campos ...
متن کاملThe Quasi-morphic Property of Group
A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic if and only if, for any ...
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.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.07.021