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## Colloquium Mathematicum

2008 | 113 | 1 | 151-168
Tytuł artykułu

### A unified approach to the Armendariz property of polynomial rings and power series rings

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A ring R is called Armendariz (resp., Armendariz of power series type) if, whenever $(∑_{i≥0} a_i x^i)(∑_{j≥0} b_j x^j) = 0$ in R[x] (resp., in R[[x]]), then $a_i b_j = 0$ for all i and j. This paper deals with a unified generalization of the two concepts (see Definition 2). Some known results on Armendariz rings are extended to this more general situation and new results are obtained as consequences. For instance, it is proved that a ring R is Armendariz of power series type iff the same is true of R[[x]]. For an injective endomorphism σ of a ring R and for n ≥ 2, it is proved that R[x;σ]/(xⁿ) is Armendariz iff it is Armendariz of power series type iff σ is rigid in the sense of Krempa.
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Tom
Numer
Strony
151-168
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wydano
2008
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autor
• Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
• Member of, Mathematics Division (Taipei Office), National Center for Theoretical Sciences
autor
• Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada A1C 5S7
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