2016
4
2
0
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Some notes on the characterization of two dimensional skew cyclic codes
2
2
A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code. It is wellknown that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/<x^s1, y^ell1>_l$. In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional skew cyclic codes.
1

1
8


Z.
Sepasdar
Ferdowsi university of Mashhad
Ferdowsi university of Mashhad
Iran
zahra.sepasdar@gmail.com
Cyclic code
two dimensional skew cyclic code
generator matrix
Weakly irreducible ideals
2
2
Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasiprimary ideals and strongly irreducible ideals. The relationships between the notions primary, quasiprimary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has been given. Also the relations between weakly irreducible ideals of $R$ and weakly irreducible ideals of localizations of the ring $R$ are also studied.
1

9
17


M.
Samiei
Department of Mathematics, Velayat University, Iranshahr, Iran.
Department of Mathematics, Velayat University,
Iran
m.samiei91@yahoo.com


H.
Fazaeli Moghimi
Department of Mathematics, University of Birjand, Birjand, Iran.
Department of Mathematics, University of
Iran
hfazaeli@birjand.ac.ir
Weakly irreducible ideal
quasiprimary ideal
strongly irreducible ideal
On two generalizations of semiprojective modules: SGQprojective and $pi$semiprojective
2
2
Let $R$ be a ring and $M$ a right $R$module with $S=End_R(M)$. A module $M$ is called semiprojective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQprojective and $pi$semiprojective modules as two generalizations of semiprojective modules. A module $M$ is called an SGQprojective module if for any $phiin S$, there exists a right ideal $X_phi$ of $S$ such that $D_S(Im phi)=phi Soplus X_phi$ as right $S$modules. We call $M$ a $pi$semiprojective module if for any $0neq sin S$, there exists a positive integer $n$ such that $s^nneq 0$ and any $R$homomorphism from $M$ to $s^nM$ can be extended to an endomorphism of $M$. Some properties of this class of modules are investigated.
1

19
29


T.
Amouzegar
Quchan university of Advanced Technology
Quchan university of Advanced Technology
Iran
t.amoozegar@yahoo.com
Semiprojective module
SGQprojective module
$pi$Semiprojective
Coretractable module
Endomorphism ring
The universal $mathcal{AIR}$ compactification of a semigroup
2
2
In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.
1

31
39


A.
Sahleh
University of Guilan
University of Guilan
Iran
sahlehj@guilan.ac.ir


L.
Najarpisheh
University of Guilan
University of Guilan
Iran
najarpisheh@gmail.com
Semitopological semigroup
(universal) semigroup compactification
distal function
weakly almost periodic function
ideal retraction property
Iprime ideals
2
2
In this paper, we introduce a new generalization of weakly prime ideals called $I$prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$prime if for $a, b in R$ with $ab in PIP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$prime ideals and study some of its properties. Moreover, we give conditions under which $I$prime ideals becomes prime or weakly prime and we construct the view of $I$prime ideal in decomposite rings.
1

41
47


I.
Akray
Soran University
Soran University
Iraq
ismaeelhmd@yahoo.com
Prime ideal
weakly prime ideal
almost prime ideal
radical of the ideal
2D skew constacyclic codes over R[x, y; ρ, θ]
2
2
For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2D skew $(lambda_1,lambda_2)$constacyclic codes in the ring $R[x,y;rho,theta]/langle x^llambda_1,y^slambda_2rangle_{mathit{l}}.$ Also, the dual of 2D skew $(lambda_1,lambda_2)$constacyclic codes is investigated.
1

49
63


H.
Mostafanasab
Eski Silahtaraga Elektrik Santrali, Kazim Karabekir, Istanbul Bilgi University
Eski Silahtaraga Elektrik Santrali, Kazim
Turkey
h.mostafanasab@gmail.com
Cyclic codes
Skew polynomial rings
2D skew constacyclic codes