|
Algebra and Discrete Mathematics, 2010, том 9, выпуск 2, страницы 78–97
(Mi adm30)
|
|
|
|
Эта публикация цитируется в 9 научных статьях (всего в 9 статьях)
RESEARCH ARTICLE
Automorphisms of finitary incidence rings
Nikolay Khripchenko V. N. Karazin Kharkiv National University, Faculty of Mathematics and Mechanics
Аннотация:
Let $P$ be a quasiordered set, $R$ an associative unital ring, $\mathcal C(P,R)$ a partially ordered category associated with the pair $(P,R)$ [6], $FI(P,R)$ a finitary incidence ring of $\mathcal C(P,R)$ [6]. We prove that the group $\mathrm{Out}FI$ of outer automorphisms of $FI(P,R)$ is isomorphic to the group $\mathrm{Out}\mathcal C$ of outer automorphisms of $\mathcal C(P,R)$ under the assumption that $R$ is indecomposable. In particular, if $R$ is local, the equivalence classes of $P$ are finite and $P=\bigcup_{i\in I}P_i$ is the decomposition of $P$ into the disjoint union of the connected components, then $\mathrm{Out}FI\cong (H^1(\overline P,C(R)^*)\rtimes\prod_{i\in I}\mathrm{Out}R)\rtimes\mathrm{Out}P$. Here $H^1(\overline P,C(R)^*)$ is the first cohomology group of the order complex of the induced poset $\overline P$ with the values in the multiplicative group of central invertible elements of $R$. As a consequences, Theorem 2 [9], Theorem 5 [2] and Theorem 1.2 [8] are obtained.
Ключевые слова:
finitary incidence algebra, partially ordered category, quasiordered set, automorphism.
Поступила в редакцию: 24.05.2010 Исправленный вариант: 08.11.2010
Образец цитирования:
Nikolay Khripchenko, “Automorphisms of finitary incidence rings”, Algebra Discrete Math., 9:2 (2010), 78–97
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm30 https://www.mathnet.ru/rus/adm/v9/i2/p78
|
Статистика просмотров: |
Страница аннотации: | 173 | PDF полного текста: | 84 | Первая страница: | 1 |
|