N Fold Hemiring » książka
N Fold Hemiring
ISBN-13: 9783639516944 / Angielski / Miękka / 2015 / 96 str.
This 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 Hemiring if (A, _1) is an abelian group (A, _2) is Monoid, (A, _3) is Monoid, ....... (A, _(n+1)) is Monoid, _2 is distributive over _1, _3 is distributive over _1, ......, _(n+1 )is distributive over _1 . 2 If A is a n-fold Hemiring 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 Hemiring is a abelian group with respect to Q2, -------, Qn+1 . 5 Any nonempty subset S of a n-fold Hemiring A = (A1 Q1, Q2, Q3, ---------, Qn+1) Is called sub n-fold Hemiring; if S = (S, Q1, Q2, --------, Qn+1) is a n-fold Hemiring . 6 A nonempty subset S of a n-fold Hemiring A is a sub n fold Hemiring of A iff"
This article covers the theoretical proofs of 1 Let A be a non-empty set and θ_1,θ_2 〖,θ〗_3,......,θ_(n+1) be binary operations on A . Then A=〖(A,θ〗_1,θ_2 〖,θ〗_3,......,θ_(n+1)) is said to be n fold Hemiring if 〖(A,θ〗_1) is an abelian group 〖 (A,θ〗_2) is Monoid , 〖 (A,θ〗_3) is Monoid , .......〖 (A,θ〗_(n+1)) is Monoid , θ_2 is distributive over θ_1 , θ_3 is distributive over θ_1 , ......, θ_(n+1 )is distributive over θ_1 . 2 If A is a n-fold Hemiring with zero element 0 Then for all a ,b ,c ϵ 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 Hemiring is a abelian group with respect to Q2 ,-------, Qn+1 . 5 Any nonempty subset S of a n-fold Hemiring A = (A1 Q1, Q2, Q3,---------,Qn+1) Is called sub n-fold Hemiring ; if S = (S, Q1,Q2,--------,Qn+1) is a n-fold Hemiring . 6 A nonempty subset S of a n-fold Hemiring A is a sub n fold Hemiring of A iff
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