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

• Autorzy: Tsiu-Kwen Lee , Yiqiang Zhou
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16S36: Ordinary and skew polynomial rings and semigroup rings
• 16S99: None of the above, but in this section
• 16U99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 113
• Numer: 1
• Strony: 151-168

Daty

wydano

2008

Twórcy

autor

Tsiu-Kwen Lee

• Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
• Member of, Mathematics Division (Taipei Office), National Center for Theoretical Sciences

autor

Yiqiang Zhou

• Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada A1C 5S7

Identyfikatory

DOI

10.4064/cm113-1-9