Geodesic
On strongly graded Gorestein orders
Algebra and discrete mathematics, no. 2 (2005), pp. 80-89

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Let $G$ be a finite group and let $\Lambda=\oplus_{g\in G}\Lambda_{g}$ 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 $K$, $\Lambda$ is an $R$-order in a separable $K$-algebra such that the algebra $\Lambda_1$ is a Gorenstein $R$-order, then $\Lambda$ is also a Gorenstein $R$-order. Moreover, we prove that the induction functor $ind:Mod\Lambda_{H}\rightarrowMod\Lambda$ defined in Section 3, for a subgroup $H$ of $G$, commutes with the standard duality functor.
Keywords: strongly graded rings, Gorenstein orders, symmetric algebras. 
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     author = {T. Theohari-Apostolidi and H. Vavatsoulas},
     title = {On strongly graded {Gorestein} orders},
     journal = {Algebra and discrete mathematics},
     pages = {80--89},
     publisher = {mathdoc},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_2_a5/}
}
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T. Theohari-Apostolidi; H. Vavatsoulas. On strongly graded Gorestein orders. Algebra and discrete mathematics, no. 2 (2005), pp. 80-89. http://geodesic.mathdoc.fr/item/ADM_2005_2_a5/