On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings

Ali, Eltiyeb

doi:10.28924/2291-8639-21-2023-108

Research Article

On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings

Eltiyeb Ali¹

a:1:{s:5:"en_US";s:18:"NAJRAN University ";}

Abstract

In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this property relates to the p.q.-Baer property of R and the existence of a generalized join in I(R) for M-indexed subsets, where I(R) denotes the set of ideals of R. Additionally, we prove a connection between R being a left p.q.-Baer ring and the CM-quasi-Armendariz property. Moreover, we prove that for any element φ²=φ, there exist an idempotent element e²=e such that φ = c_e. We then prove that R is quasi-Baer if and only if the crossed product structure R⋊M is quasi-Baer. Finally, we present novel results regarding various constructions for crossed products.

How to Cite

E. Ali, On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings, Int. J. Anal. Appl. 21 (2023), 108. https://doi.org/10.28924/2291-8639-21-2023-108

BibTeX

@article{Ali2023,
  author  = {Ali, Eltiyeb},
  title   = {On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {108},
  doi     = {10.28924/2291-8639-21-2023-108}
}

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