In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...

An element a of a commutative ring R is nilregular if and only if x is nilpotent whenever ax is nilpotent. More generally, an ideal I of R is nilregular if and only if x is nilpotent whenever ax is nilpotent for all a ∈ I. We give a direct proof that if R is Noetherian, then every nilregular ideal contains a nilregular element. In constructive mathematics, this proof can then be seen as an algo...

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphi...

In Archimedean vector lattices we show that each element of the band generated by a finite element is also finite. In vector lattices with the (PPP) and in Banach lattices we obtain some characterizations of finite elements by using the generalized order units for principal bands. In the case of Banach lattices with order continuous norm the ideal of all finite elements coincides with the linea...

We improve the zeroizing attack on the multilinear map of Garg, Gentry and Halevi (GGH). Our algorithm can solve the Graded Decisional Diffie-Hellman (GDDH) problem on the GGH scheme when the dimension n of the ideal lattice Z[X]/(X+1) is O(κλ) as suggested for the κ-linear GGH scheme. The zeroizing attack is to recover a basis of an ideal generated by a secret element g ∈ Z[X]/(X + 1) from the...

Constraints on binocular matching were investigated by comparing the thresholds for interocular correlation in random element displays for human and model observers, with element density manipulated as a parameter. The models consisted of ideal decision rules operating on the entire stimulus, only on the edges in the stimulus, or only on the sparse minority elements in the stimulus. The results...

In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold (C or complex analytic). Deformation theory of associative algebras was initiated by Gerstenhaber in [G]. A deformation of an associative algebra A over an Artinian ring a is an a-linear associative algebra structure on A⊗ a such that, for the maximal ideal m of a, A ⊗ m is a...

In this work, new oscillator topologies based on a recently introduced active element, namely inverting second-generation current conveyor, are presented. This recently introduced unity gain based active element is suitable for integrated circuit realization and can easily be implemented with CMOS technology. Considering this fact, basic oscillator topologies employing a single, two and three c...

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  ...

In this paper we show that if K is an incline with multiplicative identity and I is an r-ideal of K containing a unit u, then I = K. Moreover, we show that in a non-zero incline K with multiplicative identity and zero element, every proper r-ideal in K is contained in a maximal r-ideal of K. Z. Q. Cao, K. H. Kim and F. W. Roush [3] introduced the notion of incline algebras in their book, Inclin...