TITLE

Weak Annihilator Property of Malcev-Neumann Rings

AUTHOR(S)
OUYANG LUNQUN; LIU JINWANG
PUB. DATE
July 2013
SOURCE
Asian Academy of Management Journal of Accounting & Finance;2013, Vol. 9 Issue 2, p351
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let R be an associative ring with identity, G an totally ordered group, s a map from G into the group of automorphisms of R, and t a map from G×G to the group of invertible elements of R. The weak annihilator property of the Malcev-Neumann ring R " ((G)) is investigated in this paper. Let nil(R) denote the set of all nilpotent elements of R, and for a nonempty subset X of a ring R, let NR(X) = {a ∊ R ∣ Xa ⊆ nil(R)} denote the weak annihilator of X in R. Under the conditions that R is an NI ring with nil(R) nilpotent and s is compatible, we show that: (1) If the weak annihilator of each nonempty subset of R which is not contained in nil(R) is generated as a right ideal by a nilpotent element, then the weak annihilator of each nonempty subset of R " ((G)) which is not contained in nil(R"((G))) is generated as a right ideal by a nilpotent element. (2) If the weak annihilator of each nonnilpotent element of R is generated as a right ideal by a nilpotent element, then the weak annihilator of each nonnilpotent element of R" ((G))) is generated as a right ideal by a nilpotent element. As a generalization of left APP-rings, we next introduce the notion of weak APP-rings and give a necessary and sufficient condition under which the ring R"((G)) over a weak APP-ring R is weak APP.
ACCESSION #
88053845

 

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