SKEMA PEMBAGIAN RAHASIA DENGAN KODE LINEAR

Skema pembagian rahasia dikembangkan secara terpisah oleh Shamir dan Blakely pada tahun 1979. Sejak saat itu perkembangan skema pembagian rahasia menjadi sangat pesat. Kebanyakan dari skema adalah sistem (n,k) threshold. Pada makalah ini akan dibahas mengenai skema pembagian rahasia dengan menggunakan kode linear yang diperkenalkan oleh Massey serta beberapa hal yang terkait antara lain codeword minimal, himpunan akses minimal, dan struktur akses. Kata kunci: skema pembagian rahasia, kode linear, codeword minimal, himpunan akses minimal, struktur akse

Beberapa Sifat Modul Miskin

Modul miskin adalah modul yang injektif relatif terhadap semua modul semisederhana. Dalam tulisan ini dibahas mengenai eksistensi dan pembentukan modul miskin. Berikutnya dibahas peranan dari modul injektif yang dapat digantikan oleh modul miskin dengan tambahan sifat tertentu. [A poor module defined to be a module which injective relative only to all semisimple modules. We give the existence of poor modules, how to form poor modules over any rings.The last, we discus about the role of injective module which can be replaced by poor module with some additional properties.

Karakterisasi Modul Torsi dan Modul Bebas Torsi Menggunakan Preradikal

Dalam teori sistem abstrak, modul bebas torsi dapat digunakan untuk menentukan keterkendalian suatu sistem. Untuk itu diperlukan studi yang lebih mendalam mengenai krakteristik modul torsi dan modul bebas torsi. Di samping hasil-hasil yang sudah ada dalam teori modul, penyelidikan mengenai modul torsi maupun bebas torsi dapat dilakukan melalui sudut pandang lain, yaitu menggunakan preradikal. Preradikal adalah fungtor bagian dari fungtor identitas dengan sifat tertentu, yang dalam penelitian ini diterapkan pada kategori modul kiri atas gelanggang dengan elemen satuan. Dari sebuah preradikal dapat dibentuk kelas torsi dan kelas bebas torsi. Secara khusus, akan diambil sebagai preradikal adalah pengaitan suatu modul ke modul bagian torsinya. Kemudian penyelidikan akan dilakukan pada karakter dan sifat-sifat modul-modul anggota kelas torsi dan kelas bebas torsi yang terbentuk. Hasil utama penelitian ini adalah : 1. Terdapat modul injektif E sehingga untuk setiap modul torsi N bersifat HomR ( N , E ) = 0 . 2. Setiap modul yang bebas torsi akan di-cogenerated oleh suatu modul injektif Penelitian ini diharapkan memberi sumbangan pemikiran pada teori sistem abstrak, terutama dalam menyelidiki sifat keterkendalian sebuah sistem. Kata-kata kunci : modul torsi, modul bebas torsi, preradikal, kelas torsi, kelas bebas torsi

Fully Prime and Fully Coprime Modules

In this work we study fully prime and fully coprime modules by defining product and coproduct of fully invariant submodules in a modules and characterized them. Moreover we look over the relation between fully prime(fully coprime modules) and another definition of primeness(co-primeness) such as prime and endo prime(coprime and endo-coprime) modules. The primeness of the endomorphism ring is also interest. Keyword: fully prime modules, fully coprime module

On Total Irregularity Strength of Double-Star and Related Graphs

AbstractLet G = (V, E) be a simple and undirected graph with a vertex set V and an edge set E. A totally irregular total k-labeling f : V ∪ E → {1, 2,. . ., k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x1, their weights and are distinct, and for any two different edges xy and x1y1 their weights f (x) + f (xy) + f (y) and f (x1) + f (x1y1) + f (y1) are also distinct. A total irregularity strength of graph G, denoted byts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for double-star S n,m, n, m ≥ 3 and graph related to it, that is a caterpillar S n,2,n, n ≥ 3. The results are and ts(S n,2,n) = n

On the Graded *- rings

A prime ring A is called a ∗−ring if β(A/I) = A/I for every nonzero ideal proper I of A, where β is the prime radical. Gardner in 1988 asked whether the upper radical U(∗k) of the essential closure ∗k of the class of all ∗−rings coincide with the prime radical β. Until now, this problem remains open. In this paper, we construct a graded ∗−ring that motivates a further research to bring the Gardner problem into a graded version

On a Class of

In [Int. Electron. J. Algebra, 15, 173 (2014)], Smith introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an R-module M, i.e., μ an

On the restricted graded Jacobson radical of rings of Morita context

Abstract: The class of rings J = {A|(A, ◦) forms a group} forms a radical class and it is called the Jacobson radical class. For any ring A, the Jacobson radical J (A) of A is defined as the largest ideal of A which belongs to J . In fact, the Jacobson radical is one of the most important radical classes since it is used widely in another branch of abstract algebra, for example, to construct a two-sided brace. On the other hand, for every ring of Morita context T =(R V W S), we will show directly by the structure of the Jacobson radical of rings that the Jacobson radical J (T) = (J (R) V0 W0 J (S)), where J (R) and J (S) are the Jacobson radicals of R and S , respectively, V0 = {v ∈ V |vW ⊆ J (R)} and W0 = {w ∈ W|wV ⊆ J (S)}. This clearly shows that the Jacobson radical is an N−radical. Furthermore, we show that this property is also valid for the restricted G−graded Jacobson radical of graded ring of Morita context

Non-Braid Graphs of Ring Zn

The research in graph theory has been widened by combining it with ring. In this paper, we introduce the definition of a non-braid graph of a ring.  The non-braid graph of a ring R, denoted by YR, is a simple graph with a vertex set R\B(R), where B(R) is the set of x in R such that  xyx=yxy for all y in R.  Two distinct vertices x and y are adjacent if and only if xyx not equal to yxy.  The method that we use to observe the non-braid graphs of Zn is by seeing the adjacency of the vertices and its braider.  The main objective of this paper is to prove the completeness and connectedness of the non-braid graph of ring Zn. We prove that if n is a prime number, the non-braid graph of Zn is a complete graph. For all n greater than equal to 3,  the non-braid graph of Zn is a connected graph

*p-MODULES AND A SPECIAL CLASS OF MODULES DETERMINED BY THE ESSENTIAL CLOSURE OF THE CLASS OF ALL *-RINGS

A ring A is called a *-ring if A is a prime ring and A has no nonzero proper prime homomorphic image. The *-ring was introduced by Korolczuk in 1981. Since *-rings have an important role in radical theory of rings, the properties of *-ring have been being investigated intensively. Since every ring can be viewed as a module over itself, the generalization of *-ring into module theory is an interesting investigation. We would like to present the generalization of *-rings in module theory named *p-modules. An A-module M is called a -module if M is a prime A-module and M has no nonzero proper prime submodule. According to the result of our investigation, we show that every *-ring is a *p-module over itself. Furthermore, let A be a ring, let M be an A-module, and let I be an ideal of A with I subset (0:M)A where (0:M)A={a in A| aM={0}}. We show that M is a *p-module over A if and only if M is a *p-module over A/I. On the other hand, the essential closure *k of the class of all *-rings is a special class of rings. As the last result of our investigation, we present the special class of modules determined by *k