in this paper, we introduce the concept of semihyperring $(r,+,cdot)$ together with a suitable partial order $le$. moreover, we introduce and study hyperideals in ordered semihyperrings. simple ordered semihyperrings are defined and its characterizations are obtained. finally, we study some properties of quasi-simple and $b$-simple ordered semihyperrings.

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.

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

The aim of this paper is the study of fuzzy $Gamma$-hyperrings. In thisregard the notion of -fuzzy hyperideals of $Gamma$-hyperrings are introduced andbasic properties of them are investigated. In particular, the representationtheorem for $nu$-fuzzy hyperideals are given and it is shown that the image of a-fuzzy hyperideal of a $Gamma$-hyperring under a certain conditions is two-valued.Finally,...

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyper lter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyper lters in ternary semihypergroups. Some relationships between hype...