a simple, efficient and clean procedure has been developed for the cleavage of imines c=n bond. deprotection of imines to their parent carbonyl and amine compounds was achieved using p-toluenesulfonic acid in the solid state condition at 25-45 ˚c. the salient features of this methodology are shorter reaction times, cheap processing, high yields of product and easy availability of the catalyst. ...

In this paper, a combination of algebraic and topological methods are applied to obtain new structural results on harmonic rings. Especially, it is shown that if Gelfand ring A modulo its Jacobson radical zero dimensional ring, then clean ring. It also proved that, for given A, the retraction map $${\text {Spec}}(A)\rightarrow {\text {Max}}(A)$$ flat continuous only Dually, mp-ring {Min}}(A)$$...

the synthesis of cis-n-[a-carbobenzyloxy-b-(p-hydroxyphenyl)ethyl]-3-phthalimido-4-styryl-2-azetidinone is described. we have found that the electron-rich schiff bases can afford the cis-b-lactam ring even in the presence of the free hydroxyl functions. the mechanisms of cis and trans-b-lactam ring formation are discussed. the discussions are consistent with the recent publications.

In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

in this paper we study the structure and the commutativity of a ring r, in which for each x,y ? r, there exist two integers depending on x,y such that [x,y]k equals x n or y n.