{"product_id":"elements-of-n-fold-ring-von-manohar-durge","title":"Elements of N fold Ring","description":"\u003cp\u003eThis article covers the theoretical proof¿s 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 \u0026amp; -\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783639760798\"\u003e\u003ch3\u003eA sincere efforts towards realization\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783639760798","offer_id":39467361435741,"sku":"9783639760798","price":59.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/748cc21f-763f-48f9-9389-d88226c87a2c.jpg?v=1781411605","url":"https:\/\/shop.autorenwelt.de\/en\/products\/elements-of-n-fold-ring-von-manohar-durge","provider":"Autorenwelt Shop","version":"1.0","type":"link"}