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On strongly graded Gorestein orders

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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Main Authors: Theohari-Apostolidi, Th., Vavatsoulas, H.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2005
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/156618
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spelling 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
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