In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introd...In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sucient conditions under which an epimorphism of weak (H, A) Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.展开更多
The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-id...The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-ideal, fuzzy dot ideal and fuzzy dot H-ideals in BCH- algebras are discussed, several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals (fuzzy dot H-ideals) are studied. The relations between a fuzzy dot ideal (fuzzy dot H-ideal) in BCH-algebras and a fuzzy dot ideal (fuzzy dot H-ideal) in the product algebra of BCH-algebras are given.展开更多
Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{...Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{H,R)-pseudoalgebras are studied by generalizing the aboveconstruction when(H,R)is a quasitrianglar Hopf algebra.A tthe same time,the(H,R)-pseudoalgebra is constructed byboth the usual algebra and the tensor product o f(H,R)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed.展开更多
In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old...In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.展开更多
基金Supported by the Natural Science Foundation of Shandong Province(ZR2012AL02)
文摘In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sucient conditions under which an epimorphism of weak (H, A) Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.
基金Supported by the special item of Key Laboratory of Education Bureau of Sichuan Province(2006ZD050)
文摘The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-ideal, fuzzy dot ideal and fuzzy dot H-ideals in BCH- algebras are discussed, several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals (fuzzy dot H-ideals) are studied. The relations between a fuzzy dot ideal (fuzzy dot H-ideal) in BCH-algebras and a fuzzy dot ideal (fuzzy dot H-ideal) in the product algebra of BCH-algebras are given.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK20171348)
文摘Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{H,R)-pseudoalgebras are studied by generalizing the aboveconstruction when(H,R)is a quasitrianglar Hopf algebra.A tthe same time,the(H,R)-pseudoalgebra is constructed byboth the usual algebra and the tensor product o f(H,R)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed.
基金supported by Basic Science Research Program through the National Research Foundation of Korea (NRF)the Ministry of Education,Science and Technology (2010-0022035)
文摘In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.