2014
2
2
2
0
Triple factorization of nonabelian groups by two maximal subgroups
2
2
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of ranktwo geometry and ranktwo coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of nonabelian finite groups $D_{2n}$ and $PSL(2,2^{n})$ for their triple factorizations by finding certain suitable maximal subgroups, which these subgroups are define with original generators of these groups. The related ranktwo coset geometries motivate us to define the ranktwo coset geometry graphs which could be of intrinsic tool on the study of triple factorization of nonabelian groups.
1

1
9


A.
Gharibkhajeh
Islamic Azad University
Islamic Azad University
Iran
a_gharib@iautnb.ac.ir


H.
Doostie
Islamic Azad University
Islamic Azad University
Iran
doostih@gmail.com
Rank
Ranktwo geometry
triple factorization
two geometry
dihedral groups
projective special linear groups
projective special linear groups
A graph associated to spectrum of a commutative ring
2
2
Let $R$ be a commutative ring. In this paper, by using algebraic properties of $R$, we study the Hase digraph of prime ideals of $R$.
1

11
23


M.
Karimi
Islamic Azad University
Islamic Azad University
Iran
karimimth@bojnourdiau.ac.ir
Commutative ring
spectrum
dimension
connectedness
independent set
On a special class of StanleyReisner ideals
2
2
For an $n$gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$module $S/I$ where $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to the generalized suspension of it in the StanleyReisner sense. Applications to StanleyReisner ideals and simplicial complexes are considered.
1

25
36


K.
Borna
Kharazmi University
Kharazmi University
Iran
borna@khu.ac.ir
Betti numbers
Stanley
graded Betti numbers
Reisner ideal
graded minimal free resolution
StanleyReisner ideal
simplicial complexes
A note on primarylike submodules of multiplication modules
2
2
Primarylike and weakly primarylike submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primarylike submodules of a module lie between primary submodules and weakly primarylike submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful property.
1

37
41


H.
Fazaeli Moghimi
University of Birjand
University of Birjand
Iran
hfazaeli@birjand.ac.ir


F.
Rashedi
University of Birjand
University of Birjand
Iran
fatemehrashedi@birjand.ac.ir


M.
Samiei
University of Birjand
University of Birjand
Iran
mahdisamiei@birjand.ac.ir
Primary
Primarylike submodule
like submodule
weakly primarylike submodule
primeful property
weakly primary
multiplication module
First nonabelian cohomology of topological groups II
2
2
In this paper we introduce a new definition of the first nonabelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflationrestriction exact sequence. Also, we obtain a seventerm exact cohomology sequence up to dimension 2. We give an interpretation of the first nonabelian cohomology of a topological group by the notion of a principle homogeneous space.
1

43
61


H.
Sahleh
University of Guilan
University of Guilan
Iran
sahleh@guilan.ac.ir


H. E.
Koshkoshi
University of Guilan
University of Guilan
Iran
h.e.koshkoshi@guilan.ac.ir
Nonabelian cohomology of topological groups
cocompatible triple
partially crossed topological bimodule
principle homogeneous space
Weakly prime ternary subsemimodules of ternary semimodules
2
2
In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$ternary subsemimodule of a ternary $R$semimodule $M$, then a relation between weakly prime ternary subsemimodules of $M$ containing $N$ and weakly prime ternary subsemimodules of the quotient ternary $R$semimodule $M/N_{(Q)}$ is obtained.
1

63
72


J. N.
Chaudhari
N. M. University
N. M. University
Indian
jnchaudhari@rediffmail.com


H. P.
Bendale
N. M. University
N. M. University
Indian
hpbendale@gmail.com
Entire ternary semimodule
subtractive ternary subsemimodule
partitioning ternary subsemimodule
subtractive ternary subsemimodules
partitioning ternary subsemimodules
weakly prime ternary subsemimodule
weakly prime ternary subsemimodules
quotient ternary semimodule