This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we ...This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.展开更多
The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-alge...The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-algebra are still normed BCI-algebras. The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated. The limit notion of sequence of points in normed BCI-algebras is introduced, and its related properties are investigated.展开更多
The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive clas...The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.展开更多
As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some ...As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.展开更多
文摘This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.
基金Supported by the Special Item of Key Laboratory of Education Bureau of Sichuan Province(2006ZD050)Supported by Natural Science Foundation of China(11071178)
文摘The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-algebra are still normed BCI-algebras. The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated. The limit notion of sequence of points in normed BCI-algebras is introduced, and its related properties are investigated.
文摘The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10701019 and 10871057)the Fundamental Research Funds for the Central Universities, the ZJZSF (Grant Nos. Y607136, D7080080)+1 种基金Qianjiang Excellence Project (Grant No. 2007R10031)the New Century 151 Talent Project (2008) of Zhejiang Province
文摘As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.
