On skew power series over McCoy rings

Document Type : Research Paper

Authors

Department of Mathematics, Higher Education center of Eghlid, Eghlid, Iran

Abstract

Let R be a ring with an endomorphism α‎. ‎A ring R is a skew power series McCoy ring if whenever any non-zero power series f(x)=∑i=0∞aixi,g(x)=∑j=0∞bjxj∈R[[x;α]] satisfy f(x)g(x)=0‎, ‎then there exists a non-zero element c∈R such that aic=0‎, ‎for all i=0,1,…‎. ‎We investigate relations between the skew power series ring and the standard ring-theoretic properties‎. ‎Moreover‎, ‎we obtain some characterizations for skew power series ring R[[x;α]]‎, ‎to be McCoy‎, ‎zip‎, ‎strongly \textit{AB} and has Property (A)‎.

Keywords

References

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History

  • Receive Date: 28 March 2022
  • Revise Date: 30 May 2022
  • Accept Date: 03 August 2022

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