JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 15-24.doi: 10.6040/j.issn.1671-9352.0.2021.049

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*-Armendariz rings

LI Xin1, WANG Yao1, REN Yan-li2*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Published:2021-08-09

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Abstract: The properties of Armendariz rings with an involution are investigated, some examples of this class rings are given, and their extensions and the relationship between*-Armendariz rings and related rings are studied.

Key words: involution, *-Armendariz ring, polynomial ring, right quotient ring, Baer ring

CLC Number: 

  • O153.3
[1] BERBERIAN S K. Baer*-rings[M]. Berlin: Springer, 1972.
[2] FAKIEH W M, NAUMAN S K. Reversible rings with involutions and some minimalities[J]. Sci World J, 2013, 8:1-8.
[3] FAKIEH W M. Symmetric rings with involutions[J]. British J Math Comp Sci, 2015, 8(6):492-505.
[4] KAPLANSKY I. Rings of operatos[M]. New York: W A Benjamin, 1965.
[5] LIU Z K, ZHAO R Y. On weak Armendariz rings[J]. Comm Algebra, 2006, 34:2607-2616.
[6] ANTOINE R. Nilpotent elements and Armendariz rings[J]. J Algebra, 2008, 319(8):3128-3140.
[7] ARMENDARIZ E P. A note on extensions of Baer and P.P.-rings[J]. J Austral Math Soc, 1974, 18:470-473.
[8] FAKIEH W M.*-Skew polynomial rings[J]. British J Math Comp Sci, 2015, 10(4):1-12.
[9] ANDERSON D D, CAMILLO V. Armendariz rings and Gaussian rings[J]. Comm Algebra, 1998, 26(7):2265-2272.
[10] KIM N K, LEE Y. Extensions of reversible rings[J]. J Pure Appl Algebra, 2003, 185:207-223.
[11] HUH C, LEE Y, SMOKTUNOWICZ A. Armendariz rings and semicommutative rings[J]. Comm Algebra, 2002, 30(2):751-761.
[12] KIM N K, LEE Y. Armendariz rings and reduced rings[J]. J Algebra, 2000, 223(2):477-488.
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