A Regularity Criterion for Semigroup Rings

An analogue of the Kunz–Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings.     

Gr-凝聚环上分次W~n-模的自反性

引进了分次 wn -模 ,讨论了具有有限分次 FP-自内射维数的 gr凝聚环和分次 wn -模的自反性 .所得的结果推广了 Stentr m,Bass和黄兆泳等人的若干结果 .     

Multimode squeezed states produced by a confocal parametric oscillator

We investigate the spatial behaviour of the quantum-noise-reduction spectrum of the vacuum state emitted by a degenerate optical parametric oscillator below threshold. In view of possible experimental implementations, we consider a mode-degenerate resonator and two matching lenses and show that, for the realistic case of a finite-width pump, significant level of squeezing can be observed in a very small region of the beam. Received 25 September 2002 Published online 11 February 2003     

关于AP-内射环的一个注记

本文的主要目的是讨论AP-内射环中的两个问题:(1)环R是正则的当且仅当R是左AP-内射的左PP-环;(2)如果R是左AP-内射环,那么R是内射环当且仅当R是弱内射环.因此我们推广了内射环的一些结果,与此同时我们还取得了一些新的结果.     

The p-Blocks of the Mackey Algebra

Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding bloks of the group algebra.     

The matrix equation AXB+CYD=Eover a simple artinian ring

This paper discussed the matrix equation AXB+CYD=Eover a simple Artinian ring, obtains several necessary and sufficient conditions for existence of a solution, gives the representation of solution by g-inverses, and extends a theorem of W.E. Roth's simple Artinian rings.     

Descent Monomials, P-Partitions and Dense Garsia-Haiman Modules

A two-variable analogue of the descents monomials is defined and is shown to form a basis for the dense Garsia-Haiman modules. A two-variable generalization of a decomposition of a P-partition is shown to give the algorithm for the expansion into this descent basis. Some examples of dense Garsia-Haiman modules include the coinvariant rings associated with certain complex reflection groups.     

(H,R)-Lie coalgebras and (H,R)-Lie bialgebras

Given an (H,R)-Lie coalgebra Γ, we construct (H,R _T )-Lie coalgebra Γ^T through a right cocycle T, where (H,R) is a triangular Hopf algebra, and prove that there exists a bijection between the set of (H,R)-Lie coalgebras and the set of ordinary Lie coalgebras. We also show that if (L, [, ], Δ, R) is an (H,R)-Lie bialgebra of an ordinary Lie algebra then (L ^T , [, ], Δ_T, R _T ) is an (H,R _T )-Lie bialgebra of an ordinary Lie algebra.     

T拟内射模与TQI环

本文定义并刻划了Ｔ拟内射模与Ｔ拟内射包，证明了ＷＧ－ｃｏｃｒｉｔｉｃａｌＴ拟内射模的自同态环为正则非奇异右自内射环．最后讨论了Ｔ拟内射模与Ｔ内射模一致的环，即ＴＱＩ环．还给出了Ｇａｂｒｉｅｌ拓扑Ｇ中每个右理想Ｔ拟内射的几个等价条件