In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

Let R be a Noetherian standard N d-graded ring and M,N finitely generated, N d-graded R-modules. Let I1, . . . , Is be finitely many homogeneous ideals of R. We show that there exist linear functions f, g : Ns → Nd such that the associated primes over R0 of [Exti(N,M/I1 1 · · · I ns s M)]m and [Tori(N,M/I n1 1 · · · I ns s M)]m are stable whenever m ∈ N d satisfies m ≥ f(n1, . . . , ns) and m ≥...

We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large value of the index, each term should be divisible by a primitive prime divisor, one that has not appeared in any earlier term. Proofs of this are known in only a few cases. Weaker results in the general direction are give...

1: We study polytopes associated to factorisations of prime powers. These polytopes have explicit descriptions either in terms of their vertices or as intersections of closed halfspaces associated to their facets. We give formulae for their f−vectors. 1 Main results Polytopes have two dual descriptions: They can be given either as convex hulls of finite sets or as compact sets of the form ∩f∈Ff...

We prove that the associated variety of a Poisson prime ideal of the centre of a symplectic reflection algebra at parameter t = 0 is irreducible.

let $r$ be a commutative ring with identity‎. ‎a proper ideal $p$ of $r$ is a $(n-1,n)$-$phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin r$‎, ‎$a_1cdots a_nin pbackslash p^m$ ($a_1cdots a_nin pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin p$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎in this paper several results concerning $(n-1,n)$-$phi_m$-prime and $(n-1,n)$-...

Starting from the difficulty of creating playful representation of domain-specific abstract concepts, this study discusses the design of Prime Slaughter, a computer game aimed at facilitating individual sense-making of abstract mathematical concepts. Specifically the game proposes a transpositionmathematical concepts. Specifically the game proposes a transposition of primality and factorization...

It is shown that gas-dust perturbations in a disc with dust settling to the midplane exhibit non-linear three-wave resonant interactions between streaming wave (SDW) and two inertial waves (IW). In particular case considered this paper, SDW at wavenumber $k^\bullet = 2\kappa / (g_z t_s)$, where $\kappa$, $g_z$ $t_s$ are, respectively, epicyclic frequency, vertical gravitational acceleration par...