群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0＜ G_1＜…＜G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1)．本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖...群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0＜ G_1＜…＜G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1)．本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖远离性之推广．进一步应用极大子群和 Sylow 子群给出了有限群为可解群的一些特征．展开更多
As generalization of Clifford semigroups, left Clifford semigroups are defined and ξ-products for such semigroups and their semilattice decompositions are studied. In particular, considering how a semilattice decompo...As generalization of Clifford semigroups, left Clifford semigroups are defined and ξ-products for such semigroups and their semilattice decompositions are studied. In particular, considering how a semilattice decomposition becomes a strong semilattice decomposition and ξ-product becomes spined product, some structure theorems and characteristics for this class of semigroups are obtained.展开更多
LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC,...LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP? ? j? I Se i ,e i ?E. In particular,P is a projective, indecomposable and unitary object if and only ifP ?Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.展开更多
A commutative ring R is said to be Chinese if, given a, b 6 R and ideals A, B of R such that a ≡ b(A + B), there exists c ∈ R such that c ≡ a(A) and c ≡ b(B). Chinese rings were investigated by K.E.Aubert and I.Be...A commutative ring R is said to be Chinese if, given a, b 6 R and ideals A, B of R such that a ≡ b(A + B), there exists c ∈ R such that c ≡ a(A) and c ≡ b(B). Chinese rings were investigated by K.E.Aubert and I.Beck in 1982. However, in their paper, they said that they were unable to settle the case whether the ring Z[X] is Chinese or not. In this paper, we provide a short proof to show that the ring Z[X] is not Chinese. The techinque we used here is different from Aubert and Beck. Moreover, we show that for any algebraic numbers a1 ···, a the ring Z[a1,··· an] is Chinese for n ≥ 1.展开更多
文摘群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0＜ G_1＜…＜G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1)．本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖远离性之推广．进一步应用极大子群和 Sylow 子群给出了有限群为可解群的一些特征．
基金Proiect supported by the National Natural science Founnation of China
文摘As generalization of Clifford semigroups, left Clifford semigroups are defined and ξ-products for such semigroups and their semilattice decompositions are studied. In particular, considering how a semilattice decomposition becomes a strong semilattice decomposition and ξ-product becomes spined product, some structure theorems and characteristics for this class of semigroups are obtained.
基金Research partially supported by a UGC (HK) (Grant No. 2160092)
文摘LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP? ? j? I Se i ,e i ?E. In particular,P is a projective, indecomposable and unitary object if and only ifP ?Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.
文摘A commutative ring R is said to be Chinese if, given a, b 6 R and ideals A, B of R such that a ≡ b(A + B), there exists c ∈ R such that c ≡ a(A) and c ≡ b(B). Chinese rings were investigated by K.E.Aubert and I.Beck in 1982. However, in their paper, they said that they were unable to settle the case whether the ring Z[X] is Chinese or not. In this paper, we provide a short proof to show that the ring Z[X] is not Chinese. The techinque we used here is different from Aubert and Beck. Moreover, we show that for any algebraic numbers a1 ···, a the ring Z[a1,··· an] is Chinese for n ≥ 1.
