Graded Antisimple Primitive Radical |
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Authors: | Jun Chao Wei Li Bin Li |
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Institution: | (1) Department of Mathematics, College of Science, Yangzhou University, Yangzhou 225002, P. R. China E-mail: Lbli324@yahoo.com, CN |
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Abstract: | We introduce the graded version of the antisimple primitive radical $ {\user1{\mathcal{S}\mathcal{J}}} $ , the graded antisimple primitive radical $ {\user1{\mathcal{S}\mathcal{J}}}_{G} $ . We show that $ {\user1{\mathcal{S}\mathcal{J}}}_{G} = {\user1{\mathcal{S}\mathcal{J}}}_{{{\text{ref}}}} = {\user1{\mathcal{S}\mathcal{J}}}^{G} $ when |G| < ∞, where $ {\user1{\mathcal{S}\mathcal{J}}}_{{{\text{ref}}}} $ denotes the reflected antisimple primitive radical and $ {\user1{\mathcal{S}\mathcal{J}}}^{G} $ denotes the restricted antisimple primitive radical. Furthermore, we discuss the graded supplementing radical of $ {\user1{\mathcal{S}\mathcal{J}}}^{G} $ . |
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Keywords: | Graded antisimple primitive radical Graded subdirectly irreducible graded primitive ring Graded supplementing radical |
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