We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger. Let R = k[x1, x2, . . . , xr] be a polynomial ring over a field. We will say that an ideal I ⊆ R has the saturated chain p...

| The well known \strong pseudoprime test" has its highest probability of error (1=4) when the numbers being tested are certain Carmichael numbers with 3 prime factors. We present a non-rigorous plausibility argument that the count C3 (x) of 3-factor Carmichaels up to x, is asymptotically C3(x) K x 1=3 (ln x) ?3 where K 478 110 is an absolute constant given by K = 3 3 X 1a<b<c 1 (abc) 4=3 Y p F...

Abstract The statistical behaviour of the transport reaction progress variable variance, $$\widetilde{{c^{^{\prime\prime}2} }},$$ c ″ 2 ~ , and non-dimensiona...

let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...

let  be a banach algebra and  a derivation. in this paper, it is proved, under certain conditions, that , where  is the jacobson radical of . moreover, we prove that if  is unital and  is a continuous derivation, then , where  denotes the set of all primitive ideals such that  is commutative,  denotes the set of all maximal (modular) ideals such that  is commutative, and  is the set of all non-...

In our paper referred to above we claim to enumerate all …nite primitive linear groups of prime degree r over C with a nonabelian socle. However, the case where the socle is imprimitive was overlooked. In the present paper we deal with this case to complete the classi…cation. 2000 Mathematics Subject Classi…cation: 20H20 20C15 20C33 In the paper referred to above, we state a theorem (Theorem 1....

In this work, we study the strong decay of newly observed Pcs(4459), assuming that it is a pure $$\Xi_{c}\bar{D}^{\ast}$$ molecular state. Considering two possible spin-parity assignments JP = 1/2− and 3/2−, partial widths state into J/ψΛ, D − Λ + , $$\bar{D}\Xi_{c}^{(\prime)}$$ final states through hadronic loops are evaluated with help effective Lagrangians. comparison LHCb data, S-wave $$\ba...

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...