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 language | English |
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Pages (from-to) | 196-211 |
Journal | Journal of Algebra |
Volume | 452 |
DOIs | |
Publication status | Published - 15 Apr 2016 |
Keywords
- Finitely presented
- Jacobson radical
- Semigroup algebra
- Semigroup ring
- Semiprimitive
- Symmetric presentation
- Unique product