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

Previous Articles    

*-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

PDF (PC)

553

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.
[1] QIN Lan-lan, WANG Yao, REN Yan-li. General symmetric rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 63-68.
[2] MA Guang-lin, WANG Yao, REN Yan-li. Some extensions of T-nilpotent rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 68-73.
[3] GENG Dao-hong, WANG Yao, REN Yan-li. α-skew Armendariz rings relative to a monoid [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 1-5.
[4] GUO Ying, YAO Hai-lou. The presented dimensions of polynomial rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 71-75.
[5] WANG Yao, ZHANG Jiu-lin, REN Yan-li. On Ore extensions of nilpotent p.p.-rings and nilpotent Baer rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 76-81.
[6] LIU Chun-hui. Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 83-89.
[7] WANG Yao1, JIANG Mei-mei1, REN Yan-li2*. Some properties of skew polynomial rings#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 40-45.
[8] ZHANG Wan-ru. Skew nil McCoy rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 57-62.
[9] LIU Chun-hui1,2. Theory of filters in Fuzzy implication algebras [J]. J4, 2013, 48(09): 73-77.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd