Rings whose clean elements are uniquely strongly clean
-
Peter V. Danchev
,
Omid Hasanzadeh
Abstract
We define the class of CUSC rings, which are rings whose clean elements are uniquely strongly clean. These rings are a common generalization of the so-called USC rings, introduced by Chen–Wang–Zhou in J. Pure Appl. Algebra (2009), which are rings whose elements are uniquely strongly clean. These rings also generalize the so-called CUC rings, defined by Călugăreanu and Zhou in Mediterranean J. Math. (2023), which are rings whose clean elements are uniquely clean. We establish that a ring is USC if and only if it is simultaneously CUSC and potent. Some other interesting relationships with CUC rings are obtained as well.
Funding statement: The first-named author, P. V. Danchev, of this research paper was partially supported by the Junta de Andalucía under Grant FQM 264. The second, third and fourth authors of this research paper were partially supported by the Bonyad-e Melli-e Nokhebegan.
Acknowledgements
The authors express their sincere gratitude to the anonymous expert for the careful refereeing of the submission and the constructive suggestions on the presentation made.
References
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Articles in the same Issue
- Frontmatter
- Some results in prime rings involving endomorphisms
- On the generalized fractional Laplace–Bessel operator
- Smoothness of solutions of differential equations of constant strength in Roumieu spaces
- Rings additively generated by certain periodic elements
- Rings whose clean elements are uniquely strongly clean
- New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
- On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
- Characterization of multiplicative Jordan n-higher derivations on unital rings
- The multiplicative Lie algebra on general linear groups
- The optimal control problem for systems of integro-differential equations with finite and infinite horizon
- Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
- Nonlinear mixed Jordan-type derivations on *-algebras
- SG pseudo-differential operators in Dunkl setting
- Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
- The binary products of algebras with genetic realization
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A relationship between the structure of a quotient ring and
