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1.
In this paper,we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p,where p is an odd prime,and k is greater than or equal to 3.A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.  相似文献   

2.
We give more efficient criteria to characterise prime ideal or primary ideal.Further,we obtain the necessary and sufficient conditions that an ideal is prime or primary in real field from the Gr¨obner bases directly.  相似文献   

3.
Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠ 0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.  相似文献   

4.
Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal(right ideal,bi-ideal) is an ordered subsemigroup(resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal) by using some binary relations on S.  相似文献   

5.
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).  相似文献   

6.
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).  相似文献   

7.
In this paper,we generalize the concept of Type Ⅱ codes to arbitrary finite rings. We focus on Type Ⅱ codes over finite chain rings and use the Chinese Remainder Theorem on these codes to study Type Ⅱ codes over principal ideal rings.  相似文献   

8.
It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI(δE,T) under the action of the Galois group, where E = F(ζp^n ) and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F(ζ3).  相似文献   

9.
In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).  相似文献   

10.
We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p 3congruent to 3 modulo 4, the component e(p+1)/2of the p-Sylow subgroup of the ideal class group of Q(ζp) is trivial.  相似文献   

11.
An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.  相似文献   

12.
Let R be a 2-torsion free prime ring, d1 a nonzero derivation, -γ a generalized derivation associated with a nonzero derivation d2, U a square closed Lie ideal of R. In the present paper,we prove that if [di^2(u), u] ∈ Z(R) or γ acts as a homomorphism (or an antihomomorphism) on U, then U Z(R).  相似文献   

13.
Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols. Given two elliptic curves $E_1$,$E_2$ defined over a finite field $k$ with the same trace, there is a nonconstant isogeny $β$ from $E_2$ to $E_1$ defined over $k$. This study gives out the index of Hom$_k$($E_1$,$E_2$)$β$ as a nonzero left ideal in End$_k$($E_2$) and figures out the correspondence between isogenies and kernel ideals. In addition, some results about the non-trivial minimal degree of isogenies between two elliptic curves are also provided.  相似文献   

14.
The concept of derivations and generalized inner derivations has been generalized as an additive function δ: R→ R satisfying δ(xy) = δ(x)y xd(y) for all x,y∈R,where d is a derivation on R.Such a function δis called a generalized derivation.Suppose that U is a Lie ideal of R such that u2 ∈ U for all u ∈U.In this paper,we prove that U(C)Z(R) when one of the following holds:(1)δ([u,v]) = uov (2)δ([u,v]) uov=O(3)δ(uov) =[u,v](4)δ(uov) [u,v]= O for all u,v ∈U.  相似文献   

15.
Given a Noetherian local ring it is shown that there exists an integer such that is Gorenstein if and only if some system of parameters contained in generates an irreducible ideal. We obtain as a corollary that is Gorenstein if and only if every power of the maximal ideal contains an irreducible parameter ideal.

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16.

We study tight closure and test ideals in rings of characteristic using resolution of singularities. The notions of -rational and -regular rings are defined via tight closure, and they are known to correspond with rational and log terminal singularities, respectively. In this paper, we reformulate this correspondence by means of the notion of the test ideal, and generalize it to wider classes of singularities. The test ideal is the annihilator of the tight closure relations and plays a crucial role in the tight closure theory. It is proved that, in a normal -Gorenstein ring of characteristic , the test ideal is equal to so-called the multiplier ideal, which is an important ideal in algebraic geometry. This is proved in more general form, and to do this we study the behavior of the test ideal and the tight closure of the zero submodule in certain local cohomology modules under cyclic covering. We reinterpret the results also for graded rings.

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17.
运用局部域理论给出了奇素数p在数域K=Q(u~(1/2),v~(1/2))上的素理想分解形式,其中l是奇素数,u,v∈z~*,且u/vQ~l.  相似文献   

18.
We describe the lattice of the ideals generated by projections and prove a characterization of the ideal property for ``large" classes of crossed products of commutative -algebras by discrete, amenable groups; some applications are also given. We prove that the crossed product of a -algebra with the ideal property by a group with the ideal property may fail to have the ideal property; this answers a question of Shuzhou Wang.

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19.
We give a combinatorial proof of the Dedekind-Mertens formula by computing the initial ideal of the content ideal of the product of two generic polynomials. As a side effect we obtain a complete classification of the rank Cohen-Macaulay modules over the determinantal rings .

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20.
Let be an -dimensional regular local ring, essentially of finite type over a field of characteristic zero. Given an -primary ideal of , the relationship between the singularities of the scheme defined by and those defined by the multiplier ideals , with varying in , are quantified in this paper by showing that the Samuel multiplicity of satisfies whenever . This formula generalizes an inequality on log canonical thresholds previously obtained by Ein, Mustata and the author of this paper. A refined inequality is also shown to hold for small dimensions, and similar results valid for a generalization of test ideals in positive characteristics are presented.

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