scholarly journals On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Guo Tiexin
Keyword(s):  
Continuous Module ◽  
Random Normed Modules

Semigroups of continuous module homomorphisms on complex complete random normed modules*

2019 ◽  
Vol 59 (2) ◽  
pp. 229-250 ◽  
Author(s):  
Dang Hung Thang ◽  
Ta Cong Son ◽  
Nguyen Thinh
Keyword(s):  
Continuous Module ◽  
Random Normed Modules

scholarly journals Characterizing rings by a direct decomposition property of their modules

2006 ◽  
Vol 80 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Dinh Van Huynh ◽  
S. Tariq Rizvi
Keyword(s):  
Projective Module ◽  
Direct Decomposition ◽  
Decomposition Property ◽  
Direct Sum ◽  
Continuous Module

AbstractA module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module and a quasi-continuous module. In an earlier paper, we described the structure of rings over which every (countably generated) right module satisfies (℘*), and it was shown that such a ring is right artinian. In this note some additional properties of these rings are obtained. Among other results, we show that a ring over which all right modules satisfy (℘*) is also left artinian, but the property (℘*) is not left-right symmetric.

scholarly journals Relative injectivity and CS-modules

1994 ◽  
Vol 17 (4) ◽  
pp. 661-666
Author(s):  
Mahmoud Ahmed Kamal
Keyword(s):  
Direct Decomposition ◽  
Injective Hull ◽  
Extra Condition ◽  
Direct Sums ◽  
Direct Sum ◽  
Injective Modules ◽  
Semisimple Module ◽  
Continuous Module

In this paper we show that a direct decomposition of modulesM⊕N, withNhomologically independent to the injective hull ofM, is a CS-module if and only ifNis injective relative toMand both ofMandNare CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for quasi-injective modules. But when we confine ourselves to CS-modules we need no conditions on their socles. Then we investigate direct sums of CS-modules which are pairwise relatively inective. We show that every finite direct sum of such modules is a CS-module. This result is known for quasi-continuous modules. For the case of infinite direct sums, one has to add an extra condition. Finally, we briefly discuss modules in which every two direct summands are relatively inective.

THE RANDOM SUBREFLEXIVITY OF COMPLETE RANDOM NORMED MODULES

2012 ◽  
Vol 23 (03) ◽  
pp. 1250047 ◽  
Author(s):  
SHIEN ZHAO ◽  
TIEXIN GUO
Keyword(s):  
Random Normed Module ◽  
Convex Topology ◽  
Normed Module ◽  
Random Normed Modules

Combining respective advantages of the (ε, λ)-topology and the locally L0-convex topology we first prove that every complete random normed module is random subreflexive under the (ε, λ)-topology. Further, we prove that every complete random normed module with the countable concatenation property is also random subreflexive under the locally L0-convex topology, at the same time we also provide a counterexample which shows that it is necessary to require the random normed module to have the countable concatenation property.

Something about random normed modules

1998 ◽  
Vol 43 (7) ◽  
pp. 560-562
Author(s):  
Linhu Zhu ◽  
Cangyi Liu
Keyword(s):  
Random Normed Modules
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