Geodesic
On the semirings of skew polynomials
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 13-21
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Semirings of skew polynomials such as invariant, without nilpotent elements, Abelian, and Rickart without nilpotent elements are considered in this paper. Properties and characterizations of these semirings are obtained. 
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M. V. Babenko; V. V. Chermnykh. On the semirings of skew polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 13-21. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a1/

[1] Tuganbaev A. A., Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009

[2] Chermnykh V. V., “Funktsionalnye predstavleniya polukolets”, Fundament. i prikl. matem., 17:3 (2012), 111–227 | MR | Zbl