University of GuilanJournal of Algebra and Related Topics2345-39312220141201Triple factorization of non-abelian groups by two maximal subgroups1962ENA. GharibkhajehIslamic Azad UniversityH. DoostieIslamic Azad UniversityJournal Article20140803The 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.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312220141201A graph associated to spectrum of a commutative ring112363ENM. KarimiIslamic Azad UniversityJournal Article20140903Let $R$ 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.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312220141201On a special class of Stanley-Reisner ideals253664ENK. BornaKharazmi UniversityJournal Article20140514For 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, we<br />generalize 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.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312220141201A note on primary-like submodules of multiplication modules374165ENH. Fazaeli MoghimiUniversity of BirjandF. RashediUniversity of BirjandM. SamieiUniversity of BirjandJournal Article20140812Primary-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.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312220141201First non-abelian cohomology of topological groups II436166ENH. SahlehUniversity of GuilanH. E. KoshkoshiUniversity of GuilanJournal Article20140809In 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.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39312220141201Weakly prime ternary subsemimodules of ternary semimodules637267ENJ. N. ChaudhariN. M. UniversityH. P. BendaleN. M. UniversityJournal Article20140822In 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