Hyperbolicity of semigroup algebras. II. (English) Zbl 1209.16032
Summary: In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In part I of the present paper, [J. Algebra 319, No. 12, 5000-5015 (2008; Zbl 1148.16028)], E. Iwaki, S. O. Juriaans and A. C. Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a \(\mathbb{Z}\)-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.
MSC:
| 16U60 | Units, groups of units (associative rings and algebras) |
| 16S36 | Ordinary and skew polynomial rings and semigroup rings |
| 20M25 | Semigroup rings, multiplicative semigroups of rings |
| 20F67 | Hyperbolic groups and nonpositively curved groups |
| 16H10 | Orders in separable algebras |
| 16S34 | Group rings |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Keywords:
units; group rings; semigroup rings; hyperbolic groups; orders; unit groups; rational semigroup algebras; finite semigroupsCitations:
Zbl 1148.16028References:
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