JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (1): 1-4.doi: 10.6040/j.issn.1671-9352.0.2019.127

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Armendariz property for a group ring over the Hamiltons quaternion ring

YANG Liu, MA Jing*   

  1. Department of Mathematics, Jilin University, Changchun 130012, Jilin, China
  • Published:2020-01-10

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Abstract: The Armendariz property of group rings is discussed. It is proved that the group ring HCn is an Armendariz ring if and only if n≤2, where Cn is a cyclic group with n elements; for a torsion group T, an equivalent condition is given for the group ring HT to be an Armendariz ring. As an application, for real polynomial f(x)of degree n, it is proved that the quotient ring H［x］/(f(x))is an Armendariz ring if and only if f(x)has n real roots(counting multiplicity).

Key words: Hamiltons quaternion ring, Armendariz ring, group ring

CLC Number: 

  • O153.3
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