| 正定关联BCI—代数 |
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| 引用本文： | 孟杰,辛小龙.正定关联BCI—代数[J].纯粹数学与应用数学,1993,9(1):19-20. |
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| 作者姓名： | 孟杰 辛小龙 |
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| 作者单位： | 西北大学数学系，西北大学数学系 |
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| 摘 要： | 本文是作者［１］和［２］的继续，引入了正定关联ＢＣＩ－代数的概念，并证明了：正定关联ＧＢＣＫ－代数类和Ｐ－半单ＢＣＩ－代数类是正定关联ＢＣＩ－代数类的真子类。
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| 关 键 词： | 正定关联 可换BCI代数 BIC代数 P半单代数 |
Positive Implicative BCI-algebras |
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| MENG JIE,XIN XIAO LONG.Positive Implicative BCI-algebras[J].Pure and Applied Mathematics,1993,9(1):19-20. |
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| Authors: | MENG JIE XIN XIAO LONG |
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| Institution: | MENG JIE,XIN XIAO LONG Department of Mathematics,Northwest University,Xian,710069,China |
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| Abstract: | This note is a continuation of 1] and 2]. We introduce the concept ofpositive implicative BCI--algebras: a BCI-algebra X is said to be positive implicative if itsatisfies (x * (x * y)) * (y * x) =x * (x * (y * (y * x))). The following results are proved:The class of positive implicative BCK-algebras and the class of p--semisimple algebras areproper subclasses of the class of positive implicative BCI-algebras; Let X be a BCI-alge-bra. If its BCK--part B(X) is a positive implicativc BCK--algebra and if its pure BCI--partA(X) is a p--semisimple BCI--algebra, then X is a positive implicative BCI--algebra; ABCI--algebra is implicative iff it is both commutative and positive implicative. |
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| Keywords: | Positive implicative implicative commutative BCI-algebra |
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