@article {
author = {Pakdaman, A. and Attary, M.},
title = {A COVERING PROPERTY IN PRINCIPAL BUNDLES},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {91-98},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2018.1093},
abstract = {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 $x_0\in X$.},
keywords = {Principal bundle,covering space,covering group},
url = {http://jas.shahroodut.ac.ir/article_1093.html},
eprint = {http://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdf}
}
@article {
author = {Ebrahimpour, M. and Mirzaee, F.},
title = {ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {99-109},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2017.4332.1217},
abstract = {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.},
keywords = {Quasi-local ring, Weakly prime submodule, (n-1,n)-weakly prime submodule, ϕm-prime submodule},
url = {http://jas.shahroodut.ac.ir/article_1094.html},
eprint = {http://jas.shahroodut.ac.ir/article_1094_062414660840fa42c0c0d4ea6447a7ca.pdf}
}
@article {
author = {Barzegar, H.},
title = {SEQUENTIALLY COMPACT S-ACTS},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {111-125},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2017.4357.1218},
abstract = {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.},
keywords = {sequentially compact, $f$-pure injective,injective S-act},
url = {http://jas.shahroodut.ac.ir/article_1095.html},
eprint = {http://jas.shahroodut.ac.ir/article_1095_09001f39c3743b6d98c90f11286807eb.pdf}
}
@article {
author = {Alikhani, S. and Jafari, N.},
title = {TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {127-138},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2018.1096},
abstract = {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.},
keywords = {Total domination number,total domination polynomial,total dominating set},
url = {http://jas.shahroodut.ac.ir/article_1096.html},
eprint = {http://jas.shahroodut.ac.ir/article_1096_6bc97a7ad506ba2ec801a8f784bf5401.pdf}
}
@article {
author = {REZAEEZADEH, G. R. and AGHAJARI, Z.},
title = {ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {139-148},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2017.5274.1270},
abstract = {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.},
keywords = {SS-normal subgroup,SS-embedded subgroup,p-nilpotent group},
url = {http://jas.shahroodut.ac.ir/article_1097.html},
eprint = {http://jas.shahroodut.ac.ir/article_1097_93130e6e1cee6308e51da0e234136680.pdf}
}
@article {
author = {Estaji, A. A. and Karimi Feizabadi, A. Gh. and Abedi, M.},
title = {INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {149-161},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2017.5302.1272},
abstract = {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 $\Sigma L.$},
keywords = {Frame,essential ideal,socle,zero sets in pointfree topology,ring of real-valued continuous functions on a frame},
url = {http://jas.shahroodut.ac.ir/article_1099.html},
eprint = {http://jas.shahroodut.ac.ir/article_1099_9dfc8c0b4509368b035dd36aa8a9f7c3.pdf}
}
@article {
author = {Moniri Hamzekolaee, A. R.},
title = {A GENERALIZATION OF CORETRACTABLE MODULES},
journal = {Journal of Algebraic Systems},
volume = {5},
number = {2},
pages = {163-176},
year = {2018},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2017.5736.1287},
abstract = {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.},
keywords = {coretractable module,$overline{Z}(M)$-coretractable module,Kasch ring},
url = {http://jas.shahroodut.ac.ir/article_1100.html},
eprint = {http://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf}
}