Left APP-property of formal power series rings
Liu, Zhongkui ; Yang, Xiao Yan
Archivum Mathematicum, Tome 044 (2008), p. 185-189 / Harvested from Czech Digital Mathematics Library
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A ring $R$ is called a left APP-ring if the left annihilator $l_R(Ra)$ is right $s$-unital as an ideal of $R$ for any element $a\in R$. We consider left APP-property of the skew formal power series ring $R[[x; \alpha ]]$ where $\alpha $ is a ring automorphism of $R$. It is shown that if $R$ is a ring satisfying descending chain condition on right annihilators then $R[[x; \alpha ]]$ is left APP if and only if for any sequence $(b_0, b_1, \dots )$ of elements of $R$ the ideal $l_R$ $\big (\sum _{j=0}^{\infty }\sum _{k=0}^{\infty }R\alpha ^k(b_j)\big )$ is right $s$-unital. As an application we give a sufficient condition under which the ring $R[[x]]$ over a left APP-ring $R$ is left APP.

Publié le : 2008-01-01
Classification:  16P60,  16W60 
@article{119757,
     author = {Zhongkui Liu and Xiao Yan Yang},
     title = {Left APP-property of formal power series rings},
     journal = {Archivum Mathematicum},
     volume = {044},
     year = {2008},
     pages = {185-189},
     zbl = {1203.16031},
     mrnumber = {2462973},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119757}
}

Liu, Zhongkui; Yang, Xiao Yan. Left APP-property of formal power series rings. Archivum Mathematicum, Tome 044 (2008) pp. 185-189. http://gdmltest.u-ga.fr/item/119757/

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