University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 Triple factorization of non-abelian groups by two maximal subgroups 1 9 62 EN A. Gharibkhajeh Islamic Azad University H. Doostie Islamic Azad University Journal Article 2014 08 03 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 https://jart.guilan.ac.ir/article_62_a4af88eb7a50ab26ce9dd84f84e68652.pdf
University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 A graph associated to spectrum of a commutative ring 11 23 63 EN M. Karimi Islamic Azad University Journal Article 2014 09 03 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 https://jart.guilan.ac.ir/article_63_923b7f65560de307ebfc5b141a32cf2b.pdf
University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 On a special class of Stanley-Reisner ideals 25 36 64 EN K. Borna Kharazmi University Journal Article 2014 05 14 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, 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. Betti numbers Stanley graded Betti numbers Reisner ideal graded minimal free resolution Stanley-Reisner ideal simplicial complexes https://jart.guilan.ac.ir/article_64_af0fbdf0775d6c6eb49e2f0160e18b3e.pdf
University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 A note on primary-like submodules of multiplication modules 37 41 65 EN H. Fazaeli Moghimi University of Birjand F. Rashedi University of Birjand M. Samiei University of Birjand Journal Article 2014 08 12 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 https://jart.guilan.ac.ir/article_65_64dc07c17b067bd02a6bb19c1f10afab.pdf
University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 First non-abelian cohomology of topological groups II 43 61 66 EN H. Sahleh University of Guilan H. E. Koshkoshi University of Guilan Journal Article 2014 08 09 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 https://jart.guilan.ac.ir/article_66_401debc98c625ef131a511bc9335c425.pdf
University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 Weakly prime ternary subsemimodules of ternary semimodules 63 72 67 EN J. N. Chaudhari N. M. University H. P. Bendale N. M. University Journal Article 2014 08 22 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 https://jart.guilan.ac.ir/article_67_8ea62efaf0db5bbf026e477cc1e16995.pdf