This study was carried out to determine population structure, growth and reproduction properties of barbel. A total of 198 individuals were sampled. Ages of samples were found between I and VI years, fork lengths between 4.3 and 16.6 cm and total weights between 1.2 and 65.8 g. Length-weight relationship was calculated as W=0.0146×L2.934. Munro’s phi prime index was estimated as 1.9...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.

Let $N$ be a submodule of a module $M$ and a minimal primary decomposition of $N$ is known‎. ‎A formula to compute Baer's lower nilradical of $N$ is given‎. ‎The relations between classical prime submodules and their nilradicals are investigated‎. ‎Some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

the aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered ag-groupoids with left identity. these concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered ag-groupoids, so it seems to be interesting to study them.

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

The coprime graph of a group G is Γ_G with its set vertices and any two distinct are adjacent if only their order relatively prime. Let p be prime number, then G_p denotes the multiplicative 2×2 upper unitriangular matrices over ring integers modulo p. purposes this research to study Γ_(G_p ) find first second Zagreb eccentricity indices for p≥3. results as follows. First index )isE_1 (Γ_(G_p )...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...

Let $G$ be a finite group and $pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $Gamma(G)$ with vertex set $pi(G)$ and two distinct vertices $p$ and $q$ in $pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, we write $psim q$. Let $|G= p_1^{alpha_1}cdot p_2^{alpha_2}cdots p_k^{alpha_k}$, where $p_1