Geodesic
On the extension of pseudonorm and metrics to the semigroup ring
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 56 (2018), pp. 42-56

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In connection with the study of algebraic systems with additional structures (topology, order, norm, etc.), it sometimes becomes necessary to continue these additional structures from the ring to their over-rings. In particular, the question arises of the possibility to extend the given additional structures of a group and a ring to their group ring. This paper is devoted to the study of the possibility of extending a real-valued pseudonorm and a metric to the semigroup ring of a free monoid. The main result of the paper is a theorem that establishes sufficient conditions for the possibility of extending the pseudonorm of the ring R and the metric of the space X to such a group norm on the semigroup ring RF of the ring R and the free monoid F generated by the set X such that the topology given by this group norm is annular.
Mots-clés : pseudonorm, group norm.
Keywords: topology, semigroup ring 
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     author = {D. I. Yunusova},
     title = {On the extension of pseudonorm and metrics to the semigroup ring},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {42--56},
     publisher = {mathdoc},
     number = {56},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2018_56_a3/}
}
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D. I. Yunusova. On the extension of pseudonorm and metrics to the semigroup ring. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 56 (2018), pp. 42-56. http://geodesic.mathdoc.fr/item/VTGU_2018_56_a3/