Geodesic
Left APP-property of formal power series rings
Archivum mathematicum, Tome 44 (2008) no. 3, pp. 185-189 Cet article a éte moissonné depuis la source 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.
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.
Classification : 16P60, 16W60
Keywords: left APP-ring; skew power series ring; left principally quasi-Baer ring 
@article{ARM_2008_44_3_a1,
     author = {Liu, Zhongkui and Yang, Xiaoyan},
     title = {Left {APP-property} of formal power series rings},
     journal = {Archivum mathematicum},
     pages = {185--189},
     year = {2008},
     volume = {44},
     number = {3},
     mrnumber = {2462973},
     zbl = {1203.16031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008_44_3_a1/}
}
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Liu, Zhongkui; Yang, Xiaoyan. Left APP-property of formal power series rings. Archivum mathematicum, Tome 44 (2008) no. 3, pp. 185-189. http://geodesic.mathdoc.fr/item/ARM_2008_44_3_a1/