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| Titel: |
Two applications of maschke's theorem |
| Auteur: |
Lorenz, Martin Passman, D.S. |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 8 (1980) nr. 19 pagina's 1853-1866 |
| Jaar: |
1980 |
| Inhoud: |
Let R * G denote a crossed product of the finite group G over the ring R and let V be an R * G-module. Maschke's theorem states that if 1/∣G∣ ε R and if V is completely reducible as an R-module, then V is also completely reducible as an R * G -module. In this paper, we obtain two applications of this theorem, both under the assumption that R is semiprime with no ∣G∣ -torsion. The first concerns group actions and here we show that if G acts on R and if I is an essential right ideal of the fixed ring RG , then IR is essential in Rs. This result, in turn, simplifies a number of proofs already in the literature. The second application here is a short proof of a theorem of Fisher and Montgomery which asserts that the crossed product R * G is semiprime. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 6 van 6 gevonden artikelen
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