Beschreibung
This article covers the theoretical proofs of 1 Let A be a non-empty set and _1,_2 ,_3,_(n+1) be binary operations on A. Then A=(A,_1,_2 ,_3,_(n+1)) is said to be n fold ring if (A,_1) is an abelian group (A,_2) is semi group, (A,_3) is semi group,. (A,_(n+1)) is semi group _2 is distributive over _1, _3 is distributive over _1, , _(n+1 )is distributive over _1. 2 If A is a n-fold ring with zero element 0 Then for all a ,b ,c A 1) aQi0 = 0Qia = O, i = 2,3,----, n+1. 2) aQi(-b) = (-a)Qib = - (aQib), i =2,3, 3) (-a) Qi (-b) = aQib, i = 2131., n+1 4) aQi (bQ1(-c)) = (aQib) Q1(aQi (-c)), i = 2,3, n+1 5) (-1) Qi a = (-a), i = 2,3,., n+1. 6) (-1) Qi (-1) = 1, I = 2,3,4, n+1. 3 A finite n fold integral domain is a n-fold field. 4 The set of units in a commutative n-fold ring with unity is a abelion group with respect to Q2 ,-------, Qn+1. 5 Any nonempty subset S of a n-fold ring A = (A1 Q1, Q2, Q3,---------,Qn+1) Is called sub n-fold ring; if S = (S, Q1,Q2,--------,Qn+1) is a n-fold ring. 6 A nonempty subset S of a n-fold ring A is a subring of A iff xQ1(-y), xQiy S, x,y S & -
Autorenporträt
Students in Mathematics , has a experience of arround 20 years teaching in Tumsar(sns) , Banaras , Gondia (miet) , Nagpur ( inc ) , Warora ( anc) India ; Published arround 65+ international repute journal research articles. Established Uttakarsh Mathematical Group Warora 442907 India.
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