Journal of Algebraic SystemsJournal of Algebraic Systems
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Feed provided by Journal of Algebraic Systems. Click to visit.A COVERING PROPERTY IN PRINCIPAL BUNDLES
http://jas.shahroodut.ac.ir/article_1093_126.html
Let $p:Xlo B$ 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 $x_0in X$.Sun, 31 Dec 2017 20:30:00 +0100ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES
http://jas.shahroodut.ac.ir/article_1094_126.html
Abstract. Let m; n 2 be two positive integers, R a commutative ring with identity and M a unitary R-module. A proper submodule P of M is an (n 1; n)-m-prime ((n 1; n)-weakly prime) submodule if a1; : : : ; an1 2 R and x 2 M together with a1 : : : an1x 2 Pn(P : M)m1P (0 ̸= a1 : : : an1x 2 P) imply a1 : : : ai1ai+1 : : : an1x 2 P, for some i 2 f1; : : : ; n1g or a1:::an1 2 (P : M). In this paper we study these submodules. Some useful results and examples concerning these types of submodules are given.Sun, 31 Dec 2017 20:30:00 +0100SEQUENTIALLY COMPACT S-ACTS
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‎‎The investigation of equational compactness was initiated by‎ ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎ ‎equivalent to equational compactness‎. ‎Here we define the so‎ ‎called sequentially compact acts over semigroups and study‎ ‎some of their categorical and homological properties‎. ‎Some‎ ‎Baer conditions for injectivity of S-acts are also presented‎.Sun, 31 Dec 2017 20:30:00 +0100TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS
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Let $G = (V, E)$ 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 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 $G$. 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.Sun, 31 Dec 2017 20:30:00 +0100ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
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Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of G contained in H. In this paper, we study the inﬂuence of some SS-normal subgroups on the structure of a ﬁnite group G.Sun, 31 Dec 2017 20:30:00 +0100INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME
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A 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 $Sigma L.$Sun, 31 Dec 2017 20:30:00 +0100A GENERALIZATION OF CORETRACTABLE MODULES
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Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $overline{Z}(M)$ (for short, $overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $overline{Z}(M)$, there is a nonzero homomorphism $f:dfrac{M}{N}rightarrow M$. We investigate some conditions under which the two concepts coretractable and $overline{Z}(M)$-coretractable, coincide. For a commutative semiperfect ring $R$, we show that $R$ is $overline{Z}(R)$-coretractable if and only if $R$ is a Kasch ring. Some examples are provided to illustrate different concepts.Sun, 31 Dec 2017 20:30:00 +0100