Abstract
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.
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Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 323-338 https://doi.org/10.4213/mzm13148.
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Babenko, M.V., Chermnykh, V.V. On the Semiring of Skew Polynomials over a Bezout Semiring. Math Notes 111, 331–342 (2022). https://doi.org/10.1134/S0001434622030014
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DOI: https://doi.org/10.1134/S0001434622030014