@Article{Gharibkhajeh2014,
author="Gharibkhajeh, A.
and Doostie, H.",
title="Triple factorization of non-abelian groups by two maximal subgroups",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="2",
pages="1-9",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_62.html"
}
@Article{Karimi2014,
author="Karimi, M.",
title="A graph associated to spectrum of a commutative ring",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="2",
pages="11-23",
abstract="Let $R$ be a commutative ring. In this paper, by using algebraic properties of $R$, we study the Hase digraph of prime ideals of $R$.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_63.html"
}
@Article{Borna2014,
author="Borna, K.",
title="On a special class of Stanley-Reisner ideals",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="2",
pages="25-36",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_64.html"
}
@Article{FazaeliMoghimi2014,
author="Fazaeli Moghimi, H.
and Rashedi, F.
and Samiei, M.",
title="A note on primary-like submodules of multiplication modules",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="2",
pages="37-41",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_65.html"
}
@Article{Sahleh2014,
author="Sahleh, H.
and Koshkoshi, H. E.",
title="First non-abelian cohomology of topological groups II",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="2",
pages="43-61",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_66.html"
}
@Article{Chaudhari2014,
author="Chaudhari, J. N.
and Bendale, H. P.",
title="Weakly prime ternary subsemimodules of ternary semimodules",
journal="Journal of Algebra and Related Topics",
year="2014",
volume="2",
number="2",
pages="63-72",
abstract="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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_67.html"
}