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Algebra and Discrete Mathematics, 2015, том 19, выпуск 2, страницы 172–192
(Mi adm515)
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RESEARCH ARTICLE
Projectivity and flatness over the graded ring of normalizing elements
T. Guédénon Département de Mathématiques, Université de Ziguinchor
Аннотация:
Let $k$ be a field, $H$ a cocommutative bialgebra, $A$ a commutative left $H$-module algebra, $\operatorname{Hom}(H,A)$ the $k$-algebra of the $k$-linear maps from $H$ to $A$ under the convolution product, $Z(H,A)$ the submonoid of $\operatorname{Hom}(H,A)$ whose elements satisfy the cocycle condition and $G$ any subgroup of the monoid $Z(H,A)$. We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of normalizing elements of $A$. When $A$ is not necessarily commutative we obtain similar results over the graded ring of weakly semi-invariants of $A$ replacing $Z(H,A)$ by the set $\chi(H,Z(A)^H)$ of all algebra maps from $H$ to $Z(A)^H$, where $Z(A)$ is the center of $A$.
Ключевые слова:
projective module, flat module, bialgebra, smash product, graded ring, normalizing element, weakly semi-invariant element.
Поступила в редакцию: 23.11.2013 Исправленный вариант: 29.10.2014
Образец цитирования:
T. Guédénon, “Projectivity and flatness over the graded ring of normalizing elements”, Algebra Discrete Math., 19:2 (2015), 172–192
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm515 https://www.mathnet.ru/rus/adm/v19/i2/p172
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