- Title
- A description of incidence rings of group automata
- Creator
- Kelarev, Andrei; Passman, D.S.
- Date
- 2008
- Type
- Text; Book chapter
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/35468
- Identifier
- vital:3297
- Identifier
- ISBN:978-0-8218-4285-0
- Abstract
- Group automata occur in the Krohn-Rhodes Decomposition Theorem and have been extensively investigated in the literature. The incidence rings of group automata were introduced by the first author in analogy with group rings and incidence rings of graphs. The main theorem of the present paper gives a complete description of the structure of incidence rings of group automata in terms of matrix rings over group rings and their natural modules. As a consequence, when the ground ring is a field, we can use known group algebra results to determine when the incidence algebra is prime, semiprime, Artinian or semisimple. We also offer sufficient conditions for the algebra to be semiprimitive.
- Publisher
- Rhode Island, U.S.A. American Mathematical Society
- Relation
- Contemporary Mathematics : Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications : International Conference December 18-22, 2006, University of Madras, Chennai, India Chapter p. 27-33
- Rights
- Copyright American Mathematical Society
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Group automata; Incidence rings; Group rings
- Full Text
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