2018-08-20T16:59:24Z
http://jas.shahroodut.ac.ir/?_action=export&rf=summon&issue=138
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
A COVERING PROPERTY IN PRINCIPAL BUNDLES
A.
Pakdaman
M.
Attary
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 $x_0in X$.
Principal bundle
covering space
covering group
2018
01
01
91
98
http://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES
M.
Ebrahimpour
F.
Mirzaee
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.
Quasi-local ring, Weakly prime submodule, (n-1
n)-weakly prime submodule, ϕm-prime submodule
2018
01
01
99
109
http://jas.shahroodut.ac.ir/article_1094_062414660840fa42c0c0d4ea6447a7ca.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
SEQUENTIALLY COMPACT S-ACTS
H.
Barzegar
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.
sequentially compact
$f$-pure injective
injective S-act
2018
01
01
111
125
http://jas.shahroodut.ac.ir/article_1095_09001f39c3743b6d98c90f11286807eb.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS
S.
Alikhani
N.
Jafari
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.
Total domination number
total domination polynomial
total dominating set
2018
01
01
127
138
http://jas.shahroodut.ac.ir/article_1096_6bc97a7ad506ba2ec801a8f784bf5401.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
G. R.
REZAEEZADEH
Z.
AGHAJARI
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.
SS-normal subgroup
SS-embedded subgroup
p-nilpotent group
2018
01
01
139
148
http://jas.shahroodut.ac.ir/article_1097_93130e6e1cee6308e51da0e234136680.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME
A. A.
Estaji
A. Gh.
Karimi Feizabadi
M.
Abedi
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 $Sigma L.$
Frame
essential ideal
socle
zero sets in pointfree topology
ring of real-valued continuous functions on a frame
2018
01
01
149
161
http://jas.shahroodut.ac.ir/article_1099_9dfc8c0b4509368b035dd36aa8a9f7c3.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2018
5
2
A GENERALIZATION OF CORETRACTABLE MODULES
A. R.
Moniri Hamzekolaee
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.
coretractable module
$overline{Z}(M)$-coretractable module
Kasch ring
2018
01
01
163
176
http://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf