Geodesic
On partial skew Armendariz rings
Algebra and discrete mathematics, Tome 11 (2011) no. 1, pp. 23-45

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In this paper we consider rings $R$ with a partial action $\alpha$ of an infinite cyclic group $G$ on $R$. We introduce the concept of partial skew Armendariz rings and partial $\alpha$-rigid rings. We show that partial $\alpha$-rigid rings are partial skew Armendariz rings and we give necessary and sufficient conditions for $R$ to be a partial skew Armendariz ring. We study the transfer of Baer property, a.c.c. on right annhilators property, right p.p. property and right zip property between $R$ and $R[x;\alpha]$. We also show that $R[x;\alpha]$ and $R\langle x;\alpha\rangle$ are not necessarily associative rings when $R$ satisfies the concepts mentioned above.
Keywords: Armendariz rings, Baer rings and P.P. rings.
Mots-clés : partial actions 
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     author = {Wagner Cortes},
     title = {On partial skew {Armendariz} rings},
     journal = {Algebra and discrete mathematics},
     pages = {23--45},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_11_1_a2/}
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Wagner Cortes. On partial skew Armendariz rings. Algebra and discrete mathematics, Tome 11 (2011) no. 1, pp. 23-45. http://geodesic.mathdoc.fr/item/ADM_2011_11_1_a2/