On strongly graded Gorestein orders
Let G be a finite group and let Λ = ⊕g∈GΛg be a strongly G-graded R-algebra, where R is a commutative ring with unity. We prove that if R is a Dedekind domain with quotient field K, Λ is an R-order in a separable K-algebra such that the algebra Λ1 is a Gorenstein R-order, then Λ is also a Gorens...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2005 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156618 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On strongly graded Gorestein orders / Th. Theohari-Apostolidi, H. Vavatsoulas // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 80–89. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Let G be a finite group and let Λ = ⊕g∈GΛg be a
strongly G-graded R-algebra, where R is a commutative ring with
unity. We prove that if R is a Dedekind domain with quotient field
K, Λ is an R-order in a separable K-algebra such that the algebra
Λ1 is a Gorenstein R-order, then Λ is also a Gorenstein R-order.
Moreover, we prove that the induction functor ind : ModΛH →
ModΛ defined in Section 3, for a subgroup H of G, commutes with
the standard duality functor.
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| ISSN: | 1726-3255 |