Wa-Module
Abstract
M.A.Hassin and A.B.Hussien introduced thefollowing concept :(a,H) is called aringoverG if H is asubgroup of groupG and aϵG and a has finite order or infinite order , we called the ring (wa,+,.) ; (a,H) Ring over G where
wa= {amHan,m,nϵZ ,aϵG\H }
with two binary operation + and. Such that
am1 Han1 ,am2Han2ϵ wa , m1,m2,n1,n2 ϵZ
1-am1Han1+am2Han2 =am1+m2 Han1+n2 .
2-am1Han1 .am2Han2 =am1+m2 Han1+n2 .
In [4] , (wa,+,.) is commutative ring with unity aHa these lead us to give the definition of wa-module define on the ring which is for any commutative ring with unity element.
The main purpose of this work is to give definition of wa-module and some properties of Wa module many new and useful results are
Obtain about this concept, and we illustrate that by examples.
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References
Anderson , frank wand fuller R. kent ,1973 , Ring and categories of modules, department of ma the metics ,Eugene , oreg on .
Dwyer ,w.g and Greeuless , j.p , zool ,complete and torsion Modules
kasck .f ,1979 , modules and riugs , academic press , London
Razak ,M.Hassin and A.B. Hussien , 2011,on (a,H) . Ring over G, AL Mustanseria University, department of mathematics.
Sharpe ,D.w, 1972 , injective module ,Cambridge , university , press.
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