Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Maximal duo subrings in non-duo rings

Document Type : Original Paper

Authors
Seyed jamal Hashemi Zadeh dezfuly 1
Fatemeh Hassanzadeh 2
1 Department of Mathematics, Shahid Chamran University of Ahvaz.
2 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
10.22055/jamm.2025.50768.2422
Abstract
In this paper, we study maximal duo subrings in non-duo rings and investigate their structural properties. First, the definition and properties of maximal duo subrings are presented. Assuming, that these subrings are inverse-closed, their behavior in $ue$-rings is studied, and it is shown how certain properties of these subrings are transferred to the original ring. Furthermore, extremely duo rings, in which every element is either central or invertible, are introduced. Considering commutative rings and division rings as trivial examples of these rings, a nontrivial example is also constructed. It is shown that, in the nontrivial case, such rings are local, with the unique maximal ideal being the annihilator of the set of additive commutators of the ring. Moreover, it is proved that the quotient ring modulo this maximal ideal is a field.
Keywords
duo ring
extremely duo ring
inverse-closed subring
$ue$-ring
Subjects
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  • Receive Date 05 October 2025
  • Revise Date 14 November 2025
  • Accept Date 19 November 2025