Rings additively generated by certain periodic elements
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Huanyin Chen
Abstract
We present new characterizations of the rings additively generalized certain periodic elements (idempotent, tripotent and nilpotent). We prove that such rings are completely determined by the additive decompositions of their square elements. This improves the results of Chen and Sheibani [J. Algebra Appl. 16 (2017), 1750178] and Zhou [J. Algebra Appl. 16 (2017), 1850009].
Acknowledgements
The authors would like to thank the referees for their useful suggestions for the improvement of this paper.
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- 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
-
A relationship between the structure of a quotient ring and
Artikel in diesem Heft
- 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
-
A relationship between the structure of a quotient ring and
