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
We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rin...We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.展开更多
Let A and H be Hopf algebra,T-smash product A ■_T H generalizes twisted smash product A * H.This paper shows a necessary and sufficient condition for T-smash product module category A■_TH M to be braided monoidal ca...Let A and H be Hopf algebra,T-smash product A ■_T H generalizes twisted smash product A * H.This paper shows a necessary and sufficient condition for T-smash product module category A■_TH M to be braided monoidal category.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
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).
基金The NSF(11601005) of Chinathe Jiangsu Planned Projects(1601151C) for Postdoctoral Research Funds+1 种基金the Provincial NSF(KJ2017A040) of Anhui Provincethe Graduate Students Innovation Projects(2016141) of Anhui University of Technology
文摘We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.
文摘Let A and H be Hopf algebra,T-smash product A ■_T H generalizes twisted smash product A * H.This paper shows a necessary and sufficient condition for T-smash product module category A■_TH M to be braided monoidal category.
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.
