JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 19-23.doi: 10.6040/j.issn.1671-9352.0.2023.194

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Two kinds of McCoy group rings

AN Fangyu, CHENG Zhi*   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China
  • Published:2024-12-12

Abstract: Two kinds of McCoy group rings are studied. We prove that R[G] is a McCoy ring, where R is a McCoy ring and G is an infinite cyclic group, and Z[G] is a McCoy ring if G is a finite group. We also introduce the conception of a McCoy group ring related to its annihilator ideal, and study the properties of quotient McCoy group ring.

Key words: McCoy ring, group ring, annihilator ideal, strong annihilator ideal

CLC Number: 

  • O153.3
[1] REGE M B, CHHAWCHHARIA S. Armendariz rings[J]. Proceedings of the Japan Academy, 1997, 73(1):14-17.
[2] NIELSEN P P. Semi-commutativity and the McCoy condition[J]. Journal of Algebra, 2006, 298(1):134-141.
[3] HERMAN A, LI Yuanlin, PARMENTER M M. Trivial units for group rings with G-adapted coefficient rings[J]. Canadian Mathematical Bulletin, 2005, 48(1):80-89.
[4] LEI Zhen, CHEN Jianlong, YING Zhiling. A question on McCoy rings[J]. Bulletin of the Australian Mathematical Society, 2007, 76(1):137-141.
[5] LIU Yang, DU Xiankun. Armendariz group rings[J]. Communications in Algebra, 2017, 45(7):3052-3060.
[6] HENRY C D, SERGIO L P, STEVE S. Abelian right McCoy rings and related notions[J]. São Paulo Journal of Mathematical Sciences, 2022, 16(2):659-674.
[7] CAMILLO V, NIELSEN P P. McCoy rings and zero-divisors[J]. Journal of Pure and Applied Algebra, 2008, 212(3):599-615.
[8] LEE T K, WONG T L. On Armendariz rings[J]. Houston Journal of Mathematics, 2003, 29(3):583-593.
[9] WOODS S M. On perfect group rings[J]. Proceedings of the American Mathematical Society, 1971, 27(1):49-52.
[10] POLCINO M C, SEHGAL S K. An introduction to group rings[M]. London: Kluwer Academic Publishers, 2002.
[11] PASSMAN D S. The algebraic structure of group rings[M]. New York: Wiley-Interscience, 1977.
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