Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101A COVERING PROPERTY IN PRINCIPAL BUNDLES9198109310.22044/jas.2018.1093ENA.PakdamanDepartment of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.M.AttaryDepartment of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.Journal Article20150802Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal covering space has no connected locally trivial principal $pi(X,x_0)$-bundle, for every $x_0in X$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES99109109410.22044/jas.2017.4332.1217ENM.EbrahimpourDepartment of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan
, P.O.Box 518, Rafsanjan, IranF.MirzaeeDepartment of Mathematics, Faculty of Sciences, Shahid Bahonar University of
Kerman, Kerman, Iran.Journal Article20160516Abstract. Let m; n ≥ 2 be two positive integers, R a commutative<br /> ring with identity and M a unitary R-module. A proper<br /> submodule P of M is an (n 1; n)-Φm-prime ((n 1; n)-weakly<br /> prime) submodule if a1; : : : ; an1 2 R and x 2 M together with<br /> a1 : : : an1x 2 Pn(P : M)m1P (0 ̸= a1 : : : an1x 2 P) imply<br /> a1 : : : ai1ai+1 : : : an1x 2 P, for some i 2 f1; : : : ; n1g or a1:::an1 2<br /> (P : M). In this paper we study these submodules. Some useful<br /> results and examples concerning these types of submodules are<br /> given.Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101SEQUENTIALLY COMPACT S-ACTS111125109510.22044/jas.2017.4357.1218ENH.BarzegarDepartment of Mathematics, University of Tafresh , 3951879611, Tafresh, Iran.Journal Article20160521The investigation of equational compactness was initiated by<br /> Banaschewski and Nelson. They proved that pure injectivity is<br /> equivalent to equational compactness. Here we define the so<br /> called sequentially compact acts over semigroups and study<br /> some of their categorical and homological properties. Some<br /> Baer conditions for injectivity of S-acts are also presented.Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS127138109610.22044/jas.2018.1096ENS.AlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran.N.JafariDepartment of Mathematics, Yazd University, 89195-741 Yazd, Iran.Journal Article20160925Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the number of total dominating sets of $G$ of size $i$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identify these two<br /> vertices. Then continue in this manner inductively. We say that $G$ is obtained by point-attaching from $G_1, ldots ,G_k$ and that $G_i$'s are the primary subgraphs of $G$. <br /> In this paper, we consider some particular cases of these graphs that most of them are of importance in chemistry and study their total domination polynomials.Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS139148109710.22044/jas.2017.5274.1270ENG. R.REZAEEZADEHDepartment of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.Z.AGHAJARIDepartment of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.Journal Article20170109Abstract. A subgroup H of a group G is said to be SS-embedded<br />in G if there exists a normal subgroup T of G such that HT is<br />subnormal in G and H T ≤ H sG , where H sG is the maximal s-<br />permutable subgroup of G contained in H. We say that a subgroup<br />H is an SS-normal subgroup in G if there exists a normal subgroup<br />T of G such that G = HT and H T ≤ H SS , where H SS is an<br />SS-embedded subgroup of G contained in H. In this paper, we<br />study the inﬂuence of some SS-normal subgroups on the structure<br />of a ﬁnite group G.Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME149161109910.22044/jas.2017.5302.1272ENA. A.EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabze-
var, Iran.0000-0001-8993-5109A. Gh.Karimi FeizabadiDepartment of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan,0000-0003-2898-2678M.AbediEsfarayen University of Technology, Esfarayen, Iran.0000-0002-8763-4510Journal Article20170117A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essential ideal in $mathcal RL$ if and only if the set of isolated points of $ Sigma L$ is dense in $ Sigma L$ if and only if the intersection of any family of essential ideals is essential in $mathcal RL$. Besides, the counterpart of some results in the ring $C(X)$ is studied for the ring $mathcal RL$. For example, an ideal $E$ of $mathcal RL$ is an essential ideal if and only if $bigcap Z[E]$ is a nowhere dense subset of $Sigma L.$Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101A GENERALIZATION OF CORETRACTABLE MODULES163176110010.22044/jas.2017.5736.1287ENA. R.Moniri HamzekolaeeDepartment of Mathematics, University of Mazandaran, Babolsar, Iran0000-0002-2852-7870Journal Article20170518Let $R$ be a ring and $M$ a right $R$-module. We call $M$,<br /> coretractable relative to $overline{Z}(M)$ (for short, $overline{Z}(M)$-coretractable)<br /> provided that, for every proper submodule $N$ of $M$ containing $overline{Z}(M)$, there is<br /> a nonzero homomorphism $f:dfrac{M}{N}rightarrow M$. We investigate some conditions<br /> under which the two concepts coretractable and $overline{Z}(M)$-coretractable, coincide.<br /> For a commutative semiperfect ring $R$, we show that $R$ is $overline{Z}(R)$-coretractable<br /> if and only if $R$ is a Kasch ring. Some examples are provided to illustrate different concepts.