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http://dx.doi.org/10.4134/CKMS.2013.28.3.463

ON NIL GENERALIZED POWER SERIESWISE ARMENDARIZ RINGS  

Ouyang, Lunqun (Department of Mathematics Hunan University of Science and Technology)
Liu, Jinwang (Department of Mathematics and Applied Mathematics Huaihua University)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.3, 2013 , pp. 463-480 More about this Journal
Abstract
We in this note introduce a concept, so called nil generalized power serieswise Armendariz ring, that is a generalization of both S-Armendariz rings and nil power serieswise Armendariz rings. We first observe the basic properties of nil generalized power serieswise Armendariz rings, constructing typical examples. We next study the relationship between the nilpotent property of R and that of the generalized power series ring [[$R^{S,{\leq}}$]] whenever R is nil generalized power serieswise Armendariz.
Keywords
nil generalized power serieswise Armendariz; generalized power series ring; nilpotent property;
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