In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without ...

Library research dengan pendekatan deduksi-induksi ini bertujuan untuk mengkaji kesemiprimaan mendasar aljabar tak bebas yang dibangun secara hingga atas ring komutatif unital. Tujuan praktis penelitian adalah mengaplikasikan suatu contoh semiprima non-komutatif pada protokol autentikasi berdasarkan masalah dekomposisi. Di samping itu, lebih umum dari semiprima, hal ditunjukkan penyangkal. Hasi...

In 1961 J. Stein proposed an algorithm to compute the greatest common divisor of two integers. In this paper we point out that similar algorithms exist in the ring of integers of various quadratic number fields and also in the non-commutative ring of the Hurwitz quaternions. The implementations of the algorithms are straightforward. However the procedures vary from case to case. AMS Mathematics...

This article consists of a collection of open problems in commutative algebra. The collection covers a wide range of topics from both Noetherian and non-Noetherian ring theory and exhibits a variety of research approaches, including the use of homological algebra, ring theoretic methods, and star and semistar operation techniques. The problems were contributed by the authors and editors of this...

This work aims to introduce and study a new kind of divisor graph which is called idempotent graph, it denoted by . Two non-zero distinct vertices v1 v2 are adjacent if only , for some non-unit element We establish fundamental properties as well it’s connection with also planarity this graph.

We combine the language of monoids with preorders so as to refine some fundamental aspects classical theory factorization and prove an abstract theorem a variety applications. In particular, we obtain generalization, from cancellative Dedekind-finite (commutative or non-commutative) monoids, on "atomic factorizations" that traces back work P.M. Cohn in 1960s; recover D.D. Anderson S. Valdes-Leo...

Efficient algorithms are presented for factoring polynomials in the skew-polynomial ring F[x; σ], a non-commutative generalization of the usual ring of polynomials F[x], where F is a finite field and σ: F → F is an automorphism (iterated Frobenius map). Applications include fast functional decomposition algorithms for a class of polynomials in F[x] whose decompositions are “wild” and previously...