ORIGINAL_ARTICLE
Triple factorization of non-abelian groups by two maximal subgroups
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 rank-two geometry and rank-two 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 non-abelian 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 rank-two coset geometries motivate us to define the rank-two coset geometry graphs which could be of intrinsic tool on the study of triple factorization of non-abelian groups.
https://jart.guilan.ac.ir/article_62_a4af88eb7a50ab26ce9dd84f84e68652.pdf
2014-12-01T11:23:20
2019-04-22T11:23:20
1
9
Rank
Rank-two geometry
triple factorization
two geometry
dihedral groups
projective special linear groups
projective special linear groups
A.
Gharibkhajeh
a_gharib@iau-tnb.ac.ir
true
1
Islamic Azad University
Islamic Azad University
Islamic Azad University
LEAD_AUTHOR
H.
Doostie
doostih@gmail.com
true
2
Islamic Azad University
Islamic Azad University
Islamic Azad University
AUTHOR
ORIGINAL_ARTICLE
A graph associated to spectrum of a commutative ring
Let $R$ be a commutative ring. In this paper, by using algebraic properties of $R$, we study the Hase digraph of prime ideals of $R$.
https://jart.guilan.ac.ir/article_63_923b7f65560de307ebfc5b141a32cf2b.pdf
2014-12-01T11:23:20
2019-04-22T11:23:20
11
23
Commutative ring
spectrum
dimension
connectedness
independent set
M.
Karimi
karimimth@bojnourdiau.ac.ir
true
1
Islamic Azad University
Islamic Azad University
Islamic Azad University
LEAD_AUTHOR
ORIGINAL_ARTICLE
On a special class of Stanley-Reisner ideals
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 Stanley-Reisner sense. Applications to Stanley-Reisner ideals and simplicial complexes are considered.
https://jart.guilan.ac.ir/article_64_af0fbdf0775d6c6eb49e2f0160e18b3e.pdf
2014-12-01T11:23:20
2019-04-22T11:23:20
25
36
Betti numbers
Stanley
graded Betti numbers
Reisner ideal
graded minimal free resolution
Stanley-Reisner ideal
simplicial complexes
K.
Borna
borna@khu.ac.ir
true
1
Kharazmi University
Kharazmi University
Kharazmi University
LEAD_AUTHOR
ORIGINAL_ARTICLE
A note on primary-like submodules of multiplication modules
Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like 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.
https://jart.guilan.ac.ir/article_65_64dc07c17b067bd02a6bb19c1f10afab.pdf
2014-12-01T11:23:20
2019-04-22T11:23:20
37
41
Primary
Primary-like submodule
like submodule
weakly primary-like submodule
primeful property
weakly primary
multiplication module
H.
Fazaeli Moghimi
hfazaeli@birjand.ac.ir
true
1
University of Birjand
University of Birjand
University of Birjand
LEAD_AUTHOR
F.
Rashedi
fatemehrashedi@birjand.ac.ir
true
2
University of Birjand
University of Birjand
University of Birjand
AUTHOR
M.
Samiei
mahdisamiei@birjand.ac.ir
true
3
University of Birjand
University of Birjand
University of Birjand
AUTHOR
ORIGINAL_ARTICLE
First non-abelian cohomology of topological groups II
In this paper we introduce a new definition of the first non-abelian 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 inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-abelian cohomology of a topological group by the notion of a principle homogeneous space.
https://jart.guilan.ac.ir/article_66_401debc98c625ef131a511bc9335c425.pdf
2014-12-01T11:23:20
2019-04-22T11:23:20
43
61
Non-abelian cohomology of topological groups
cocompatible triple
partially crossed topological bimodule
principle homogeneous space
H.
Sahleh
sahleh@guilan.ac.ir
true
1
University of Guilan
University of Guilan
University of Guilan
LEAD_AUTHOR
H. E.
Koshkoshi
h.e.koshkoshi@guilan.ac.ir
true
2
University of Guilan
University of Guilan
University of Guilan
AUTHOR
ORIGINAL_ARTICLE
Weakly prime ternary subsemimodules of ternary semimodules
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.
https://jart.guilan.ac.ir/article_67_8ea62efaf0db5bbf026e477cc1e16995.pdf
2014-12-01T11:23:20
2019-04-22T11:23:20
63
72
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
J. N.
Chaudhari
jnchaudhari@rediffmail.com
true
1
N. M. University
N. M. University
N. M. University
LEAD_AUTHOR
H. P.
Bendale
hpbendale@gmail.com
true
2
N. M. University
N. M. University
N. M. University
AUTHOR