On one-sided $\mathcal{U}$-ideals in monoidal categories

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P. O. Box 1796, Fez, Morocco.

10.48308/cgasa.2026.241633.1571

Abstract

In this paper, we investigate one-sided (thick) ideals in monoidal categories and explore related concepts, including generating sets, idempotency, radicality and primeness. We establish several structural properties of one-sided ideals, drawing analogies with the ring-theoretic setting. Further results are obtained by specializing to pivotal categories. In particular, one-sided negligible objects are shown to provide examples of one-sided ideals, thanks to the well-established theory of categorical traces in this framework. Moreover, we introduce and study a generalization, called one-sided $\mathcal{U}$-ideals, where we show their nontrivial nature and establish various $\mathcal{U}$-analogues of the preceding results, examining the validity of several fundamental properties.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 06 June 2026

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