On the Semiring of Skew Polynomials over a Bezout Semiring

In the paper, we study the semiring of skew polynomials over a Rickart Bezout semiring. Namely, let every left annihilator ideal of a semiring be an ideal. Then the semiring of skew polynomials is a semiring without nilpotent elements, and every its finitely generated left monic ideal is principal if and only if is a left Rickart left Bezout semiring, is a rigid endomorphism, and is invertible for any nonzerodivisor . We also obtain a characterization of the semiring in terms of Pierce stalks of the semiring . The structure of left monic ideals of the semiring of skew polynomials over a left Rickart left Bezout semiring is clarified.