The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by...The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if （A, C, ψ） is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and （α, β ）-Yetter-Drinfeld modules as examples.展开更多
Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduc...Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B#y / to be a monoidal Hom-bialgebra is given. In addition, let （H, a） be a Hom-σ- Hopf algebra with Hom-〇 --antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B#y H with the antipode S defined by S（b×h）=（1B×SH（a^-1）b（-1）））（SB（b（0））×1H to be a monoidal Hom-Hopf algebra is derived.展开更多
In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain ...In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.展开更多
For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring ...For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.展开更多
In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and re...In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20060286006)the National Natural Science Founda-tion of China(No.10571026)
文摘The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if （A, C, ψ） is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and （α, β ）-Yetter-Drinfeld modules as examples.
基金The National Natural Science Foundation of China(No.11371088,10871042,11571173)the Fundamental Research Funds for the Central Universities(No.KYLX15_0105)
文摘Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B#y / to be a monoidal Hom-bialgebra is given. In addition, let （H, a） be a Hom-σ- Hopf algebra with Hom-〇 --antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B#y H with the antipode S defined by S（b×h）=（1B×SH（a^-1）b（-1）））（SB（b（0））×1H to be a monoidal Hom-Hopf algebra is derived.
基金Supported by the National Natural Science Foundation of China（11047030, 11171055） Supported by the Grant from China Scholarship Counci1（2011841026）
文摘In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.
基金partially supported by the Provincial Natural Science Foundation of Anhui Province of China（KJ2017A040）
文摘For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.
文摘In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).
