Geodesic
On the Semiring of Skew Polynomials over a Bezout Semiring
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 323-338

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In the paper, we study the semiring of skew polynomials over a Rickart Bezout semiring. Namely, let every left annihilator ideal of a semiring $S$ be an ideal. Then the semiring of skew polynomials $R=S[x,\varphi]$ is a semiring without nilpotent elements, and every its finitely generated left monic ideal is principal if and only if $S$ is a left Rickart left Bezout semiring, $\varphi$ is a rigid endomorphism, and $\varphi(d)$ is invertible for any nonzerodivisor $d$. We also obtain a characterization of the semiring $R$ in terms of Pierce stalks of the semiring $S$. The structure of left monic ideals of the semiring of skew polynomials over a left Rickart left Bezout semiring is clarified.
Keywords: semiring of skew polynomials, Bezout semiring, Rickart semiring, monic ideal, Pierce stalk of a semiring. 
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     author = {M. V. Babenko and V. V. Chermnykh},
     title = {On the {Semiring} of {Skew} {Polynomials} over a {Bezout} {Semiring}},
     journal = {Matemati\v{c}eskie zametki},
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M. V. Babenko; V. V. Chermnykh. On the Semiring of Skew Polynomials over a Bezout Semiring. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 323-338. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a0/