Archimedean domains of skew generalized power series

Ryszard Mazurek

doi:10.1515/forum-2019-0187

Published by De Gruyter April 22, 2020

Archimedean domains of skew generalized power series

Ryszard Mazurek

From the journal Forum Mathematicum

https://doi.org/10.1515/forum-2019-0187

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Abstract

A skew generalized power series ring R⁢[[S,ω,≤]] consists of all functions from a strictly ordered monoid (S,≤) to a ring R whose support is artinian and narrow, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of this ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal’cev–Neumann series rings, the “unskewed” versions of all of these, and generalized power series rings. In this paper, we characterize the skew generalized power series rings R⁢[[S,ω,≤]] that are left (right) Archimedean domains in the case where the order ≤ is total, or ≤ is semisubtotal and the monoid S is commutative torsion-free cancellative, or ≤ is trivial and S is totally orderable. We also answer four open questions posed by Moussavi, Padashnik and Paykan regarding the rings in the title.

Keywords: Skew generalized power series ring; Archimedean ring; strictly ordered monoid; Archimedean monoid

MSC 2010: 16S35; 16S36; 16W60; 06F05; 13F25; 13G05

Communicated by Manfred Droste

Funding source: Politechnika Bialostocka

Award Identifier / Grant number: WZ/WI/1/2019

Funding statement: This research was supported by the Bialystok University of Technology Grant WZ/WI/1/2019 funded from the resources for research by the Ministry of Science and Higher Education of Poland.

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Received: 2019-07-20

Published Online: 2020-04-22

Published in Print: 2020-07-01

Archimedean domains of skew generalized power series

Abstract

References

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