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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| Дата: | 2005 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156618 |
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irk-123456789-1566182019-06-20T01:27:42Z On strongly graded Gorestein orders Theohari-Apostolidi, Th. Vavatsoulas, H. 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. 2005 Article 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. 1726-3255 2000 Mathematics Subject Classification: 16H05, 16G30, 16S35, 16G10, 16W50. http://dspace.nbuv.gov.ua/handle/123456789/156618 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Theohari-Apostolidi, Th. Vavatsoulas, H. |
| spellingShingle |
Theohari-Apostolidi, Th. Vavatsoulas, H. On strongly graded Gorestein orders Algebra and Discrete Mathematics |
| author_facet |
Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_sort |
Theohari-Apostolidi, Th. |
| title |
On strongly graded Gorestein orders |
| title_short |
On strongly graded Gorestein orders |
| title_full |
On strongly graded Gorestein orders |
| title_fullStr |
On strongly graded Gorestein orders |
| title_full_unstemmed |
On strongly graded Gorestein orders |
| title_sort |
on strongly graded gorestein orders |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156618 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT theohariapostolidith onstronglygradedgoresteinorders AT vavatsoulash onstronglygradedgoresteinorders |
| first_indexed |
2023-05-20T17:50:17Z |
| last_indexed |
2023-05-20T17:50:17Z |
| _version_ |
1796154208659963904 |