Triple factorization of non-abelian groups by two maximal subgroups
A.
Gharibkhajeh
Islamic Azad University
author
H.
Doostie
Islamic Azad University
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
2
no.
2014
1
9
https://jart.guilan.ac.ir/article_62_a4af88eb7a50ab26ce9dd84f84e68652.pdf
A graph associated to spectrum of a commutative ring
M.
Karimi
Islamic Azad University
author
text
article
2014
eng
Let $R$ be a commutative ring. In this paper, by using algebraic properties of $R$, we study the Hase digraph of prime ideals of $R$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
2
no.
2014
11
23
https://jart.guilan.ac.ir/article_63_923b7f65560de307ebfc5b141a32cf2b.pdf
On a special class of Stanley-Reisner ideals
K.
Borna
Kharazmi University
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
2
no.
2014
25
36
https://jart.guilan.ac.ir/article_64_af0fbdf0775d6c6eb49e2f0160e18b3e.pdf
A note on primary-like submodules of multiplication modules
H.
Fazaeli Moghimi
University of Birjand
author
F.
Rashedi
University of Birjand
author
M.
Samiei
University of Birjand
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
2
no.
2014
37
41
https://jart.guilan.ac.ir/article_65_64dc07c17b067bd02a6bb19c1f10afab.pdf
First non-abelian cohomology of topological groups II
H.
Sahleh
University of Guilan
author
H. E.
Koshkoshi
University of Guilan
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
2
no.
2014
43
61
https://jart.guilan.ac.ir/article_66_401debc98c625ef131a511bc9335c425.pdf
Weakly prime ternary subsemimodules of ternary semimodules
J. N.
Chaudhari
N. M. University
author
H. P.
Bendale
N. M. University
author
text
article
2014
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
2
v.
2
no.
2014
63
72
https://jart.guilan.ac.ir/article_67_8ea62efaf0db5bbf026e477cc1e16995.pdf