| 3阶CI-代数 |
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| 引用本文： | 孟彪龙.3阶CI-代数[J].西安科技大学学报,2012,32(1):127-129. |
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| 作者姓名： | 孟彪龙 |
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| 作者单位： | 西安科技大学理学院,陕西西安,710054 |
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| 摘 要： | 作为BCK/BCI/BCH-代数和BE-代数的推广,CI-代数是一类新的逻辑代数。构造CI-代数的实例是亟待解决的问题。扩张已有代数是构造新代数的重要方法。给出了两个扩张定理,分别把BE-代数扩张为BE-代数,把CI-代数扩张为CI-代数,并且给出了全部3阶的CI-代数,检验了3阶(2,0)型代数的81个乘法表,同构代数视作相等的,则仅有8个代数是3阶的CI-代数,为CI-代数的研究提供了重要实例。
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| 关 键 词： | BE-代数 CI-代数 强CI-代数 |
CI-algebras of order 3 |
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| MENG Biao-long.CI-algebras of order 3[J].JOurnal of XI’an University of Science and Technology,2012,32(1):127-129. |
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| Authors: | MENG Biao-long |
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| Institution: | MENG Biao-long(College of Scineces,Xi’an University of Science and Technology,Xi’an 710054,China) |
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| Abstract: | CI-algebras are a new class of logical algebras as a generalization of BCK/BCI/BCH-algebras.It is a problem to be solved to construct examples of CI-algebras.Extensions of algebraic structures are an important way to construct new algebras.In the present paper,we give two extension theorems(i.e.,Theorems 2.1 and 2.2)and all CI-algebras of order 3.Theorem 2.1 extends BE-algebras to BE-algebras,Theorem 2.2 extends CI-algebras to CI-algebras.We check 81 multiplication tables of order 3 with type(2,0),in which there are only 8 CI-algebras.This provides important examples to investigate CI-algebras. |
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| Keywords: | CI-algebra BE-algebra strong CI-algebra |
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