Abstract:
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.
Keywords:pseudonorm, topology, semigroup ring, group norm.
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