Algebraic prime subalgebras in simple Artinian algebras |
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| Authors: | Tsiu-Kwen Lee Yiqiang Zhou |
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| Affiliation: | a Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
b Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Nfld A1C 5S7, Canada |
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| Abstract: | We prove a Wedderburn-Artin type theorem for algebraic prime subalgebras in simple Artinian algebras, giving a generalized version of Yahaghi’s theorem [B.R. Yahaghi, On F-algebras of algebraic matrices over a subfield F of the center of a division ring, Linear Algebra Appl. 418 (2006) 599-613]. We also show that every semiprime left algebraic subring in a semiprime right Goldie ring must be a semiprime Artinian ring. |
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| Keywords: | 16P60 16N60 16K40 |
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