Abstract
Necessary and sufficient conditions are given for a prime Noetherian algebra K[S] of a submonoid S of a polycyclic-by-finite group G to be a maximal order. These conditions are entirely in terms of the monoid S. This extends earlier results of Brown concerned with the group ring case and of the authors for the case where K[S] satisfies a polynomial identity.
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Dedicated to Fred Van Oystaeyen, on the occasion of his sixtieth birthday.
Research partially supported by the Onderzoeksraad of Vrije Universiteit Brussel, Fonds voor Wetenschappelijk Onderzoek (Flanders), Flemish-Polish bilateral agreement BIL2005/VUB/06 and a MNiSW research grant N201 004 32/0088 (Poland).
Research funded by a Ph.D. grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).
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Goffa, I., Jespers, E. & Okniński, J. Semigroup Algebras of Submonoids of Polycyclic-by-Finite Groups and Maximal Orders. Algebr Represent Theor 12, 357–363 (2009). https://doi.org/10.1007/s10468-009-9152-7
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DOI: https://doi.org/10.1007/s10468-009-9152-7