Semirings of skew Laurent polynomials

The paper considers semirings of skew polynomials and semirings of skew Laurent polynomials with rigid endomorphism. It is shown that the semiring $S$ is $\varphi$-rigid if and only if the semiring of skew Laurent polynomials $S[x^{-1},x,\varphi]$ is a semiring without nilpotent elements. The concept of the $\varphi$-arm-semiring is introduced. It is proved that if $S$ is a $\varphi$-arm-semiring, then $S$ is Baer (left Rickart) exactly when $S[x^{-1},x,\varphi]$ is a Baer (resp. left Rickart) semiring.