In this paper we obtain asymptotic expansion for the geometric mean of values positive strongly multiplicative function $f$ satisfying $f(p)=\alpha(d)\,p^d+O(p^{d-\delta})$ any prime $p$ with $d$ real and $\alpha(d),\delta>0$.

In this paper we prove that if the congruence lattice of an automaton A is finite then the endomorphism semigroup E(A) of A is finite. Moreover, if A is commutative then A is A-finite. We prove that if 3 ≤ |A| then a commutative automaton A is simple if and only if it is a cyclic permutation automaton of prime order. We also give some results concerning cyclic, strongly connected and strongly t...

We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite langua...

In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a fu...

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d'subseteq m$ such that $n+d'$ is a strongly dense submodule of $m$...

OBJECTIVE Following a meaningful prime stimulus, schizophrenia patients have been hypothesized to exhibit impaired neurophysiological activation of related concepts in general, and/or supranormal activation of weakly related concepts in particular, within semantic memory. The former abnormality may occur at longer intervals, and the latter at shorter intervals, after the prime. The authors test...

In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...

 Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

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...