Geodesic
Semirings of skew Laurent polynomials
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 521-533

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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, Armendariz semiring, Baer semiring, Rickart semiring.
Mots-clés : rigid endomorphism 
@article{SEMR_2020_17_a8,
     author = {D. A. Maslyaev and V. V. Chermnykh},
     title = {Semirings of skew {Laurent} polynomials},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {521--533},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a8/}
}
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D. A. Maslyaev; V. V. Chermnykh. Semirings of skew Laurent polynomials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 521-533. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a8/