Units in orders and integral semigroup rings

✍ Scribed by Ann Dooms; Eric Jespers; Stanley Orlando Juriaans

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 155 KB
• Volume: 265
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00283-7

✦ Synopsis

We continue the investigations on the finite conjugacy centre, denoted as (U(Γ )), the hyper centre, and thus also the second centre Z 2 (U(Γ )), of the unit group U(Γ ) of a Z-order Γ in a finite-dimensional Q-algebra. In particular, it is shown that (U(Γ )) is finitely generated and Z 2 (U(Γ )) ⊆ (U(Γ )), also conditions are obtained for these two groups to be equal or central. Applications are given to the unit group of the integral semigroup ring ZS of a finite semigroup. It follows that often U(ZS) has central height two and Z 2 (U(ZS)) = (U(ZS)). This extends earlier results on integral group rings by Arora and Passi, Bovdi, Jespers and Juriaans, and Li and Parmenter.