2018-12-11T06:46:23Z
https://jart.guilan.ac.ir/?_action=export&rf=summon&issue=15
Journal of Algebra and Related Topics
2345-3931
2345-3931
2014
2
2
Triple factorization of non-abelian groups by two maximal subgroups
A.
Gharibkhajeh
H.
Doostie
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.
Rank
Rank-two geometry
triple factorization
two geometry
dihedral groups
projective special linear groups
projective special linear groups
2014
12
01
1
9
https://jart.guilan.ac.ir/article_62_a4af88eb7a50ab26ce9dd84f84e68652.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2014
2
2
A graph associated to spectrum of a commutative ring
M.
Karimi
Let $R$ be a commutative ring. In this paper, by using algebraic properties of $R$, we study the Hase digraph of prime ideals of $R$.
Commutative ring
spectrum
dimension
connectedness
independent set
2014
12
01
11
23
https://jart.guilan.ac.ir/article_63_923b7f65560de307ebfc5b141a32cf2b.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2014
2
2
On a special class of Stanley-Reisner ideals
K.
Borna
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.
Betti numbers
Stanley
graded Betti numbers
Reisner ideal
graded minimal free resolution
Stanley-Reisner ideal
simplicial complexes
2014
12
01
25
36
https://jart.guilan.ac.ir/article_64_af0fbdf0775d6c6eb49e2f0160e18b3e.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2014
2
2
A note on primary-like submodules of multiplication modules
H.
Fazaeli Moghimi
F.
Rashedi
M.
Samiei
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.
Primary
Primary-like submodule
like submodule
weakly primary-like submodule
primeful property
weakly primary
multiplication module
2014
12
01
37
41
https://jart.guilan.ac.ir/article_65_64dc07c17b067bd02a6bb19c1f10afab.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2014
2
2
First non-abelian cohomology of topological groups II
H.
Sahleh
H. E.
Koshkoshi
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.
Non-abelian cohomology of topological groups
cocompatible triple
partially crossed topological bimodule
principle homogeneous space
2014
12
01
43
61
https://jart.guilan.ac.ir/article_66_401debc98c625ef131a511bc9335c425.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2014
2
2
Weakly prime ternary subsemimodules of ternary semimodules
J. N.
Chaudhari
H. P.
Bendale
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.
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
2014
12
01
63
72
https://jart.guilan.ac.ir/article_67_8ea62efaf0db5bbf026e477cc1e16995.pdf