| 关于单BCI－代数的一些结果 |
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| 引用本文： | 刘用麟,林大华.关于单BCI－代数的一些结果[J].数学研究,1995(1). |
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| 作者姓名： | 刘用麟 林大华 |
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| 作者单位： | 福建南平师专，福建福州师专 |
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| 摘 要： | 本文讨论了单ＢＣＩ－代数．证明了一个ＢＣＩ－代数是单的当且仅当它的子代数都是单的；给出了单ｐ－半单ＢＣＩ－代数的一种表示式；证明了一个ｐ－半单ＢＣＩ－代数是单的当且仅当它的阶是素数；这样得到了一批（无限多个）单ＢＣＩ－代数；证明了商ＢＣＫ－代数Ｘ／Ａ是单的当且仅当Ａ是Ｘ的极大理想．
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| 关 键 词： | 单BCI－代数，单BCK－代数，单P－半单BCI－代数 |
SOME RESULTS ON SIMPLE BCI-ALGEBRAS |
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| Liu Yonglin, Lin Dahua.SOME RESULTS ON SIMPLE BCI-ALGEBRAS[J].Journal of Mathematical Study,1995(1). |
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| Authors: | Liu Yonglin Lin Dahua |
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| Institution: | Liu Yonglin; Lin Dahua(Nanpings Teachers Collage) (Fuzhou Teachers College) |
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| Abstract: | In ths paper,we study the structure of simple BCI-atgebras. We show that a BCI-algebra is simple if and only if its subalgebras are all simple. We give an expression of the structure of simple p-semisimple BCI-algebras. We show that a p-semisimple BCI-algebra is simple if and only if its order is prime. Thus we obtain a lot of (infinite)simple BCI-algebras. We show that quotient BCK-algebra X/A is simple if and only if A is maximal ideal of X. |
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| Keywords: | simple BCI-algebras simple BCK-algebras simple p-semisimple |
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