A COVERING PROPERTY IN PRINCIPAL BUNDLES
A.
Pakdaman
Department of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.
author
M.
Attary
Department of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.
author
text
article
2018
eng
Let $p:X\lo B$ 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 $x_0\in X$.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
91
98
http://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdf
dx.doi.org/10.22044/jas.2018.1093
ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES
M.
Ebrahimpour
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan
, P.O.Box 518, Rafsanjan, Iran
author
F.
Mirzaee
Department of Mathematics, Faculty of Sciences, Shahid Bahonar University of
Kerman, Kerman, Iran.
author
text
article
2018
eng
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)-Φm-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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
99
109
http://jas.shahroodut.ac.ir/article_1094_062414660840fa42c0c0d4ea6447a7ca.pdf
dx.doi.org/10.22044/jas.2017.4332.1217
SEQUENTIALLY COMPACT S-ACTS
H.
Barzegar
Department of Mathematics, University of Tafresh , 3951879611, Tafresh, Iran.
author
text
article
2018
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
111
125
http://jas.shahroodut.ac.ir/article_1095_09001f39c3743b6d98c90f11286807eb.pdf
dx.doi.org/10.22044/jas.2017.4357.1218
TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS
S.
Alikhani
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
author
N.
Jafari
Department of Mathematics, Yazd University, 89195-741 Yazd, Iran.
author
text
article
2018
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
127
138
http://jas.shahroodut.ac.ir/article_1096_6bc97a7ad506ba2ec801a8f784bf5401.pdf
dx.doi.org/10.22044/jas.2018.1096
ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
G. R.
REZAEEZADEH
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
author
Z.
AGHAJARI
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
author
text
article
2018
eng
Abstract. A subgroup H of a group G is said to be SS-embeddedin G if there exists a normal subgroup T of G such that HT issubnormal 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 subgroupH is an SS-normal subgroup in G if there exists a normal subgroupT of G such that G = HT and H \ T ≤ H SS , where H SS is anSS-embedded subgroup of G contained in H. In this paper, westudy the inﬂuence of some SS-normal subgroups on the structureof a ﬁnite group G.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
139
148
http://jas.shahroodut.ac.ir/article_1097_93130e6e1cee6308e51da0e234136680.pdf
dx.doi.org/10.22044/jas.2017.5274.1270
INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME
A. A.
Estaji
Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabze-
var, Iran.
author
A. Gh.
Karimi Feizabadi
Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan,
author
M.
Abedi
Esfarayen University of Technology, Esfarayen, Iran.
author
text
article
2018
eng
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 $\Sigma L.$
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
149
161
http://jas.shahroodut.ac.ir/article_1099_9dfc8c0b4509368b035dd36aa8a9f7c3.pdf
dx.doi.org/10.22044/jas.2017.5302.1272
A GENERALIZATION OF CORETRACTABLE MODULES
A. R.
Moniri Hamzekolaee
Department of Mathematics, University of Mazandaran, Babolsar, Iran
author
text
article
2018
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
5
v.
2
no.
2018
163
176
http://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf
dx.doi.org/10.22044/jas.2017.5736.1287