Putra, Mochamad David Andika (2010) A study of δQuasiBaer ring. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract
ENGLISH :
Items that is studied at abstraction algebra basically about set and its operation, and always equivalent with a nonempty set which have elements are operated with one or more binary operation. A set is provided with one or more binary operation is called algebra structure. Algebra structure with one binary operation which fulfill the certain natures is called group. While for nonempty set with two binary operations which fulfill the certain natures is called ring. At other algebra structure is also studied about QuasiBaer ring. Let R is QuasiBaer ring if the right annihilator of every ideal (as a right ideal) is generated by idempotent.
Continuing from QuasiBaer ring can be developed to become some discussions, those are δQuasiBaer ring. Let δ be a derivation on R. A ring R is called δQuasiBaer ring if the right annihilator rR (X) = {c∈R} ⃒dc = 0, ∀d∈X} of every δideal of R is generated by idempotent. Let δ : R → R is derivation of R, that is, δ is an additive map such that, so that the extension of δ : R → R is δ ̅ (αb) = δ(α)b  δα(b),∀α,b∈R. For a ring R with a derivation δ, there exists a derivation on S = R[x; δ] which extends δ. Considering an inner derivation δ on S by x defined by δ ̅ (f(x))= xf(x)  f(x)x,∀f(x)∈S .Then, δ ̅ (f(x))= δ(α_0)+...+ δ(α_n)x^n for all f(x)=α_0+...+α_n x^n∈S and δ ̅ (r)= δ(r), ∀r∈R which means that δ ̅ is an extension of δ. We call such a derivation δ ̅ on S an extended derivation of δ. For each α∈R and nonnegative integer n, there exist t_0 ,..., t_n ∈Z such that x^n α = ∑_(i=0)^n t_i δ^n=i(α)x^i. Let R[x; δ] is the polynomial ring whose elements are the polynomials denote ∑_(i=0)^n r_i x^i ∈R, where the multiplication operation by xb = bx + δ(b),∀b ∈R. Three commonly used operations for polynomials are addition “ + “, multiplication “ . ” and composition “ ◦ “. Observe that (R[x], +, .) is a ring and (R[x], +, ◦) is a left nearring where the substitution indicates substitution of f(x) into g(x), explicitly f(x) .. g(x) = f(g(x) for each f(x), g(x), explicitly f(x)◦g(x) = f(g(x) for each f(x), g(x) ∈ R[x]. At other researcher is suggested to perform a research morely about δ QuasiBaer ring, with searching natures of others.
Item Type:  Thesis (Undergraduate)  

Supervisor:  Irawan, Wahyu Henky and Abidin, Munirul  
Contributors: 


Departement:  Fakultas Sains dan Teknologi > Jurusan Matematika  
Depositing User:  Durrotun Nafisah  
Date Deposited:  13 Jun 2017 10:01  
Last Modified:  19 Jun 2023 14:02  
URI:  http://etheses.uinmalang.ac.id/id/eprint/6616 
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