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 $p:X\lo B$ 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 $x_0\in X$.https://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdfShahrood 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.https://jas.shahroodut.ac.ir/article_1094_062414660840fa42c0c0d4ea6447a7ca.pdfShahrood 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.https://jas.shahroodut.ac.ir/article_1095_09001f39c3743b6d98c90f11286807eb.pdfShahrood 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.https://jas.shahroodut.ac.ir/article_1096_6bc97a7ad506ba2ec801a8f784bf5401.pdfShahrood 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.0000-0002-0442-7269Z.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.https://jas.shahroodut.ac.ir/article_1097_93130e6e1cee6308e51da0e234136680.pdfShahrood 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 $\Sigma L.$https://jas.shahroodut.ac.ir/article_1099_9dfc8c0b4509368b035dd36aa8a9f7c3.pdfShahrood 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.https://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf