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 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.
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 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.
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 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.
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 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.
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 $M$, 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.
http://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf
coretractable module
$overline{Z}(M)$-coretractable module
Kasch ring