Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C ^*-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E ^*(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E ^*) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].      

Morita Equivalence for Rings with Involution

We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. We also prove that two commutative rings with involution are Morita *-equivalent if and only if they are *-isomorphic.     

Synthesis of dihydropyrazolo[4,3-c]azepines via iodine-mediated intramolecular hydrative cyclization

A straightforward approach to substituted dihydropyrazolo[4,3-c]azepines via I₂-mediated intramolecular hydration in pyrazole-based allylamines prepared from Morita–Baylis–Hillman adducts of 4-iodopyrazolealdehyes is described.     

群分次环和Morita等价

设Ｒ是Ｇ－分次环，Ｈ是Ｇ的子群，本文通过构造两个Ｍｏｒｉｔａｃｏｎｔｅｘｔ，给出了环Ｂ｛Ｈ｝Ｍｏｒｉｔａ等价于Ｒ＿Ｈ，Ｒ＃Ｇ￣＊Ｍｏｒｉｔａ等价于Ｒ＿Ｈ＃Ｈ￣＊的充分必要条件．     

Palladium-catalyzed nucleophilic allylic substitution of Morita–Baylis–Hillman adducts with enamines: Synthesis of 1,5-dicarbonyl compounds

An efficient nucleophilic allylic substitution of a variety of Morita–Baylis–Hillman adducts with enamines catalyzed by Pd(OAc)₂ in the presence of ZnBr₂ as a promoter is described in the present study. The reaction gives S_N2-type 1,5-dicarbonyl compounds that may subsequently undergo an intramolecular conjugate addition onto the enone moiety affording the corresponding 1,4-adducts. All the synthesized compounds have been isolated in moderate to good yields and fully characterized.     

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.     

Efficient One-Pot Synthesis of 2-Carbonyl- 1-indanols by Palladium-Catalyzed Tandem Heck–Aldol Reaction

2-Carbonyl-1-indanols were synthesized in moderate to good yields by the reaction of orthohalogenated aryl aldehyde with Morita–Baylis–Hillman adducts via a one-pot, palladium-catalyzed tandem Heck–aldol reaction. Various Morita–Baylis–Hillman adducts were examined to find the scope and limitations of this process.