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1.
K. Varadarajan 《Acta Mathematica Hungarica》1998,78(1-2):1-9
Erika Mares introduced the concepts of semi-perfectness and perfectness for projective modules, generalised the structure theorems of H. Bass and obtained results on the endomorphism rings of such modules. The present author has carried out an extensive study of endomorphism rings of various types of modules with two of his collaborators [3], [9]. In particular the concept of semi-perfectness was extended to modules not necessarily projective and results similar to those of Erika Mares obtained for quasi-projective semi-perfect modules. The object of the present paper is to extend the concept of perfectness to modules which are not necessarily projective and obtain results similar to those of Erika Mares, Roger Ware etc. concerning these modules. 相似文献
2.
Ravi Varadarajan 《BIT Numerical Mathematics》1990,30(3):450-463
We introduce a new kind of graph called multi-edge graph which arises in many applications such as finite state Markov chains and broadcasting communication networks. A cluster in such a graph is a set of nodes such that for any ordered pair of nodes, there is a path of multi-edges from one to the other such that these edges remain within the same set. We give two algorithms to partition a multi-edge graph into maximal clusters. Both these algorithms are based on the depth-first search algorithm to find strongly connected components of the directed graph. We also discuss some applications of clustering in multi-edge graphs. 相似文献
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Sankareswaran Srimurugan Paulsamy Suresh Thirukkallam Kanthadai Varadarajan 《合成通讯》2013,43(15):2483-2490
A facile method for the synthesis of (2R,3R)‐1,4‐dimethoxy‐1,1,4,4‐tetrasubstituted‐2,3‐butanediols involving oxidative cleavage of benzylidene acetal as a key step is described. These sterically hindered diols unusually formed cyclic sulfites as the major product under methanesulfonylation reaction conditions. 相似文献
6.
P. B. Ruikar M. S. Nagar M. S. Subramanian K. K. Gupta N. Varadarajan R. K. Singh 《Journal of Radioanalytical and Nuclear Chemistry》1995,201(2):125-134
The extraction of plutonium(IV), uranium(VI), zirconium(IV), europium(III) and ruthenium(III) with -pre-irradiated n-dodecane solutions of methylbutyl substituted hexanamide (MBHA), octanamide (MBOA) and decanamide (MBDA) from 3.5M HNO3 has been studied as a function of absorbed dose up to 184×104 Gray. The distribution ratios (Kd) of uranium(VI) decreased gradually up to a dose of 50×104 Gray and became almost constant thereafter, while ruthenium(III) and europium(III) were not extracted in the entire dose range studied. The Kd values of Pu(IV) decreased gradually up to 10×104 Gray, for MBOA, and 30×104 Gray for MBHA and MBDA and then increased up to a dose of 72×104 Gray, indicating the synergistic effect of radiolytic products at higher doses. The extraction of zirconium(IV) was found to increase gradually up to 72×104 Gray. However, the steep fall in Kd values of plutonium(IV), zirconium(IV) beyond a dose of 72×104 Gray was atrributed to third phase formation. The radiolytic degradation of amides was monitored by quantitative IR spectroscopy and was found to follow the order MBOA>MBDA>MBHA at 184×104 Gray having the amines and carboxylic acids as the main radiolytic products. 相似文献
7.
K. Varadarajan 《代数通讯》2013,41(2):771-783
The main results proved in this paper are: 1. For any non-zero vector space V Dover a division ring D, the ring R= End(V D) is hopfian as a ring 2. Let Rbe a reduced π-regular ring &; B(R) the boolean ring of idempotents of R. If B(R) is hopfian so is R.The converse is not true even when Ris strongly regular. 3. Let Xbe a completely regular spaceC(X) (resp. C ?(X)) the ring of real valued (resp. bounded real valued) continuous functions on X. Let Rbe any one of C(X) or C ?(X). Then Ris an exchange ring if &; only if Xis zero dimensional in the sense of Katetov. for any infinite compact totally disconnected space X C(X) is an exchange ring which is not von Neumann regular. 4. Let Rbe a reduced commutative exchange ring. If Ris hopfian so is the polynomial ring R[T 1,…,T n] in ncommuting indeterminates over Rwhere nis any integer ≥ 1. 5. Let Rbe a reduced exchange ring. If Ris hopfian so is the polynomial ring R[T]. 相似文献
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K. Varadarajan 《Proceedings Mathematical Sciences》2000,110(2):133-136
Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring
to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF. 相似文献
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