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Владикавказский математический журнал, 2007, том 9, номер 2, страницы 3–8
(Mi vmj90)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
On a decomposition equality in modular group rings
P. V. Danchev Plovdiv State University «Paissii Hilendarski», Plovdiv, Bulgaria
Аннотация:
Let $G$ be an abelian group such that $A\le G$ with $p$-component $A_p$ and $B\le G$, and let $R$ be a commutative ring with 1 of prime characteristic $p$ with nil-radical $N(R)$. It is proved that if $A_p\not\subseteq B_p$ or $N(R)\ne 0$, then $S(RG)=S(RA)(1+I_p(RG;B))$ $\iff$ $G=AB$ and $G_p=A_pB_p$. In particular, if $A_p\ne 1$ or $N(R)\ne 0$, then $S(RG)=S(RA)\times (1+I_p(RG;B))$ $\iff$ $G=A\times B$. So, the question concerning the validity of this formula is completely exhausted. The main statement encompasses both the results of this type established by the author in (Hokkaido Math. J., 2000) and (Miskolc Math. Notes, 2005). We also point out and eliminate in a concrete situation an error in the proof of a statement due to T. Zh. Mollov on a decomposition formula in commutative modular group rings (Proceedings of the Plovdiv University-Math., 1973).
Ключевые слова:
direct factors, decompositions, normed unit groups, homomorphisms.
Поступила в редакцию: 03.07.2006
Образец цитирования:
P. V. Danchev, “On a decomposition equality in modular group rings”, Владикавк. матем. журн., 9:2 (2007), 3–8
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/vmj90 https://www.mathnet.ru/rus/vmj/v9/i2/p3
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