eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
91
98
10.22044/jas.2018.1093
1093
A COVERING PROPERTY IN PRINCIPAL BUNDLES
A. Pakdaman
a.pakdaman@gu.ac.ir
1
M. Attary
m_atari1989@yahoo.com
2
Department of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.
Department of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.
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 $x_0in X$.
http://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdf
Principal bundle
covering space
covering group
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
99
109
10.22044/jas.2017.4332.1217
1094
ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES
M. Ebrahimpour
m.ebrahimpour@vru.ac.ir
1
F. Mirzaee
mirzaee0269@yahoo.com
2
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan , P.O.Box 518, Rafsanjan, Iran
Department of Mathematics, Faculty of Sciences, Shahid Bahonar University of Kerman, Kerman, Iran.
Abstract. 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.
http://jas.shahroodut.ac.ir/article_1094_062414660840fa42c0c0d4ea6447a7ca.pdf
Quasi-local ring, Weakly prime submodule, (n-1
n)-weakly prime submodule, ϕm-prime submodule
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
111
125
10.22044/jas.2017.4357.1218
1095
SEQUENTIALLY COMPACT S-ACTS
H. Barzegar
h56bar@tafreshu.ac.ir
1
Department of Mathematics, University of Tafresh , 3951879611, Tafresh, Iran.
The 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.
http://jas.shahroodut.ac.ir/article_1095_09001f39c3743b6d98c90f11286807eb.pdf
sequentially compact
$f$-pure injective
injective S-act
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
127
138
10.22044/jas.2018.1096
1096
TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS
S. Alikhani
alikhani@yazd.ac.ir
1
N. Jafari
nasrin7190@yahoo.com
2
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
Department of Mathematics, Yazd University, 89195-741 Yazd, Iran.
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<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.
http://jas.shahroodut.ac.ir/article_1096_6bc97a7ad506ba2ec801a8f784bf5401.pdf
Total domination number
total domination polynomial
total dominating set
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
139
148
10.22044/jas.2017.5274.1270
1097
ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
G. R. REZAEEZADEH
gh.rezaeezadeh@yahoo.com
1
Z. AGHAJARI
z.aghajari@stu.sku.ac.ir
2
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord, Iran.
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord, Iran.
Abstract. 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.
http://jas.shahroodut.ac.ir/article_1097_93130e6e1cee6308e51da0e234136680.pdf
SS-normal subgroup
SS-embedded subgroup
p-nilpotent group
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
149
161
10.22044/jas.2017.5302.1272
1099
INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME
A. A. Estaji
aaestaji@hsu.ac.ir
1
A. Gh. Karimi Feizabadi
akarimi@gorganiau.ac.ir
2
M. Abedi
abedi@esfarayen.ac.ir
3
Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabze- var, Iran.
Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan,
Esfarayen University of Technology, Esfarayen, Iran.
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 $Sigma L.$
http://jas.shahroodut.ac.ir/article_1099_9dfc8c0b4509368b035dd36aa8a9f7c3.pdf
Frame
essential ideal
socle
zero sets in pointfree topology
ring of real-valued continuous functions on a frame
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2018-01-01
5
2
163
176
10.22044/jas.2017.5736.1287
1100
A GENERALIZATION OF CORETRACTABLE MODULES
A. R. Moniri Hamzekolaee
a.monirih@umz.ac.ir
1
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Let $R$ 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.
http://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf
coretractable module
$overline{Z}(M)$-coretractable module
Kasch ring