This article is cited in 2 papers

Mathematical logic, algebra and number theory

Semirings of skew Laurent polynomials

D. A. Maslyaev^a, V. V. Chermnykh<sup>b

a</sup> Komi Republican Academy of State Service and Management, 11, Kommunisticheskaya str., Syktyvkar, 167982, Russia
^b Piritim Sorokin Syktyvkar State University, 55, Octyabrskyi ave., Syktyvkar, 167001, Russia

Abstract: 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.

Keywords: skew polynomial semiring, skew Laurent polynomial semiring, rigid endomorphism, Armendariz semiring, Baer semiring, Rickart semiring.

UDC: 512.55

MSC: 16Y60

Received July 8, 2019, published April 8, 2020

DOI: 10.33048/semi.2020.17.033

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