Construction of a two unique product semigroup defined by permutation relations of quaternion type

Ferran Cedó, Eric Jespers, Georg Klein

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

© 2016 Elsevier Inc.. For a regular representation H⊆Symn of the generalized quaternion group of order n=4k, with k≥2, the monoid Sn(H) presented with generators a1, a2, . . ., an and with relations a1a2⋯an=aσ(1)aσ(2)⋯aσ(n), for all σ∈H, is investigated. It is shown that Sn(H) has the two unique product property. As a consequence, for any field K, the monoid algebra K[Sn(H)] is a domain with trivial units which is semiprimitive.
Original languageEnglish
Pages (from-to)196-211
JournalJournal of Algebra
Volume452
DOIs
Publication statusPublished - 15 Apr 2016

Keywords

  • Finitely presented
  • Jacobson radical
  • Semigroup algebra
  • Semigroup ring
  • Semiprimitive
  • Symmetric presentation
  • Unique product

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