JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 28-32.doi: 10.6040/j.issn.1671-9352.0.2021.809

Previous Articles    

The quasi-Baer property of the *-skew polynomial rings

WANG Yao1, QIN Lan-lan1, 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:2023-02-12

PDF (PC)

336

Abstract: The *-principally quasi-Bear property and quasi-Bear-*-property of the *-skew polynomial rings are investigated. It is proved that(1)Let R be a *-right principally quasi-Baer ring, if re=0 implies that re*=0 for any e∈S*l(R) and r∈R, then R［x;*］ is a *-right principally quasi-Baer ring;(2)Let * be a true involution on R and R be *-reversible, then R［x;*］ is a quasi-Baer *-ring if and only if R is a quasi-Baer *-ring.

Key words: involution, *-skew polynomial ring, *-principally quasi-Baer ring, quasi-Baer *-ring

CLC Number: 

  • O153
[1] BERBERIAN S K. Baer *-rings[M]. New York: Grund Mathe Wisse, 1972.
[2] FAKIEH W M, NAUMAN S K. *-skew polynomial rings[J]. British J Math Comp Sci, 2015, 10(4):1-12.
[3] BIRKENMEIER G F, KIM J Y, PARK J K. Polynomial extensions of Baer and quasi-Baer rings[J]. J Pure Appl Algebra, 2001, 159(1):25-42.
[4] ARMENDARIZ E P. A note on extensions of Baer and p.p.-rings[J]. J Austral Math Soc, 1974(18):470-473.
[5] BIRKENMEIER G F, KIM J Y, PARK J K. Principally quasi-Baer rings[J]. Comm Algebra, 2001, 29(2):639-660.
[6] FAKIEN W M, NAUMAN S K. Reversible rings with involutions and some minimalities[J]. Sci World J, 2013, 2013:1-8.
[1] LI Xin, WANG Yao, REN Yan-li. *-Armendariz rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 15-24.
[2] 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.
[3] 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