##### A COVERING PROPERTY IN PRINCIPAL BUNDLES

A. Pakdaman; M. Attary

Volume 5, Issue 2 , January 2018, Pages 91-98
##### 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 ...  Read More

##### ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES

M. Ebrahimpour; F. Mirzaee

Volume 5, Issue 2 , January 2018, Pages 99-109
##### 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; : : : ; an􀀀1 2 R and x 2 M together with a1 : : : an􀀀1x 2 Pn(P : M)m􀀀1P ...  Read More

##### SEQUENTIALLY COMPACT S-ACTS

H. Barzegar

Volume 5, Issue 2 , January 2018, Pages 111-125
##### 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 ...  Read More

##### TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

S. Alikhani; N. Jafari

Volume 5, Issue 2 , January 2018, Pages 127-138
##### 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 ...  Read More

##### ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS

Volume 5, Issue 2 , January 2018, Pages 139-148
##### 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 ...  Read More

##### INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME

A. A. Estaji; A. Gh. Karimi Feizabadi; M. Abedi

Volume 5, Issue 2 , January 2018, Pages 149-161
##### 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 ...  Read More

##### A GENERALIZATION OF CORETRACTABLE MODULES

A. R. Moniri Hamzekolaee

Volume 5, Issue 2 , January 2018, Pages 163-176
##### 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 ...  Read More