有足够幂等元的群分次环上的Morita对偶

首先定义了具有足够幂等元的群分次环的Ｓｍ ａｓｈ 积并讨论其性质,其次,借助Ｓｍ ａｓｈ 积给出了这类分环上的分次Ｍｏｒｉｔａ对偶的刻划．     

FUZZY IDEALS OF GROUP GRADED RINGS AND THEIR SMASH PRODUCTS

ABSTRACT

We prove the fuzzy analogoues of the Orbit Problem, Incomparability and Going down problem for group graded rings and their smash products.     

Graded rings and essential ideals

LetG be a group andA aG-graded ring. A (graded) idealI ofA is (graded) essential ifI⊃J≠0 wheneverJ is a nonzero (graded) ideal ofA. In this paper we study the relationship between graded essential ideals ofA, essential ideals of the identity componentA _e and essential ideals of the smash productA#G ^*. We apply our results to prime essential rings, irredundant subdirect sums and essentially nilpotent rings.     

L-R smash products for multiplier Hopf algebras

The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies Delvaux＇s main theorem in the case of smash products.     

关于分次本质右理想

设 Ｒ是 Ｇ－分次,本文讨论了环 Ｒ的相关环 Ｒ,Ｒ＃ Ｇ^*, Ｒｅ, Ｑ（Ｒ）, Ｒ^G, Ｒ*Ｇ及 Ｒ的正规化扩张Ｓ的非奇异性,右一致性,右基座之间的关系．当Ｒ_Ｒ是ＹＪ－内射模时,证明了Ｊ（Ｒ）＝Ｚ（Ｒ）。     

G-集分次模与Morita Context

对任意群Ｇ， Ｈ≤Ｇ，［１］研究了Ｇ－分次环Ｒ与有限可迁Ｇ－集的ｓｍａｓｈ积.在本文中我们对任意可迁Ｇ－集，讨论了一个关于Ｒ（Ｈ）与ｓｍａｓｈ积Ｒ＃Ｇ／Ｈ的Ｍｏｒｉｔａ ｃｏｎｔｅｘｔ，从而推广了［２］，［３］，［４］给出的关于Ｇ－分次环及其与群Ｇ的ｓｍａｓｈ积的一些重要结果．     

分次Morita对偶，Morita对偶与Smash积

设Ｃ和ｒ都是群，是Ｇ－型分次环，是Γ－型分次环．是双分次模，Ｒ＃Ｇ是Ｒ的Ｓｍａｓｈ积，Ａ＃Γ是Ａ的Ｓｍａｓｈ积。令Ｗ＝（＿ｇＵ＿（σ－１））＿（ｇ，σ）即（ｇ，σ）位置取＿ｇＵ＿（σ－１）的元素的｜Ｇ｜×｜Γ｜矩阵的全体组成的集合，且每个矩阵的每行和每列的非零元只有有限个，按矩阵运算，Ｗ构成（Ｒ＃６，Ａ＃Γ）双模。则＿ＲＵ＿Ａ定义了一个分次Ｍｏｒｉｔａ对偶当且仅当＿（Ｒ＃Ｇ）Ｗ＿（Ａ＃Γ）定义了一个Ｍｏｒｉｔａ对偶。     

分次环的Smash积A#G*与单位分量Ae理想间的对应

本文对任意群G上的任意分次环A,建立了Smash积A#G^*和单位分量A_e理想间的对应关系,并运用所建立的对应关系研究分次环的Smash积A#G^*和A_e的半素性,素性和单性.     

The absolutely Koszul property of Veronese subrings and Segre products

Absolutely Koszul algebras are a class of rings over which any finite graded module has a rational Poincaré series. We provide a criterion to detect non-absolutely Koszul rings. Combining the criterion with Macaulay2 computations, we identify large families of Veronese subrings and Segre products of polynomial rings which are not absolutely Koszul. In particular, we classify completely the absolutely Koszul algebras among Segre products of polynomial rings, when the base field has characteristic 0.     

The Relative Properties of Graded Ring R and Smash Product R # G

ＴｈｅＲｅｌａｔｉｖｅＰｒｏｐｅｒｔｉｅｓｏｆＧｒａｄｅｄＲｉｎｇＲａｎｄ　ＳｍａｓｈＰｒｏｄｕｃｔＲ＃ＧＷｅｉＪｕｎｃｈａｏ（魏俊潮）；ＬｉＬｉｂｉｎ（李立斌）（ＹａｎｇｚｈｏｕＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｙａｎｇｚｈｏｕ，２２５０...     

Hopf代数胚上的Smash积的Maschke型定理和Morita关系

本文研究了Hopf代数胚上的Smash积代数.利用Hopf代数胚的积分理论,获得了Hopf代数胚上的Smash的Maschke型定理并构造了一个Morita关系,推广了Cohen和Fishman在文献[1]中的相应结果.作为应用,获得了Hopf代数胚上的余模代数的Maschke型定理.     

The global dimension of L-R twisted smash products

We construct the new algebra A#H of an H-bimodule algebra A called the L-R twisted smash product, and give the duality theorem for L-R twisted smash products which extends the duality theorem for smash products given by Blattner and Montgomery. Furthermore, by using the duality theorem for L-R twisted smash products, we establish the relationship of global dimension between the H-bimodule algebra A and its L-R twisted smash product A#H.     

乘子Hopf代数的广义交叉积与L-R smash积(英文)

In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.     

Algebra retracts and Stanley–Reisner rings

In a paper from 2002, Bruns and Gubeladze conjectured that graded algebra retracts of polytopal algebras over a field k are again polytopal algebras. Motivated by this conjecture, we prove that graded algebra retracts of Stanley–Reisner rings over a field k are again Stanley–Reisner rings. Extending this result further, we give partial evidence for a conjecture saying that monomial quotients of standard graded polynomial rings over k descend along graded algebra retracts.     

On the Cohen-Macaulay modules of graded subrings

We give several characterizations for the linearity property for a maximal Cohen-Macaulay module over a local or graded ring, as well as proofs of existence in some new cases. In particular, we prove that the existence of such modules is preserved when taking Segre products, as well as when passing to Veronese subrings in low dimensions. The former result even yields new results on the existence of finitely generated maximal Cohen-Macaulay modules over non-Cohen-Macaulay rings.

     

Duality theorem for weak L-R smash products

This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.     

半群分次环上的Morita对偶

本文主要研究了半群分次环上的Morita对偶问题,讨论了半群分次模范畴上满足某种条件的对偶函子与双分次双模之间的等价关系.得到重要定理：半群双分次$R$-$A$双模$Q$定义一个半群分次Morita对偶当且仅当${}_RQ_A$是分次忠实平衡的,且${\rm Ref}({}_RQ)$, ${\rm Ref}(Q_A)$对分次子模和分次商模是封闭的.