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1.
The Maximal Graded Left Quotient Algebra of a Graded Algebra1)   总被引:1,自引:0,他引:1  
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A-modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.  相似文献   

2.
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   

3.
关于有限群的S-半置换子群   总被引:1,自引:0,他引:1       下载免费PDF全文
Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under the assumption that every member in Md(Gp) is S-semipermutable in G for each prime divisor p of |G| and a Sylow p-subgroup Gp of G.  相似文献   

4.
Let G be a finite group with a non-central Sylow r-subgroup R, Z(G) the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z(G)=1 and the G-conjugacy class size of every element of N is either 1 or m.  相似文献   

5.
This paper considers such a group G which possesses nontrivial proper subgroups H 1 ,H 2 such that any proper subgroup of G not contained in H 1 ∪ H 2 is p-closed and obtains that if G is soluble,then the number of prime divisors contained in |G| is 2,3 or 4;if not,then it has a form x N where N/Φ(N) is a non-abelian simple group.Then the structure of such a group is determined for p = 2,H 1 = H 2 under some conditions.  相似文献   

6.
Is it true tliat Lie homomorpHisin (isomorphism) \phi of a ring R into a ring R' is a homomorphism (isomorpliism) ? Herstein,I. N. and Kleinfeld, E. and Martindal, W. S.. obtained some results for simple ring and primitive ring,. In this paper I shall study the Lie homomorphism on the associative ring and arrive at the following main conclusion: Theorem. Suppose that R,R' are both associative rings with 1,and the center ofR’ does not contain zero divisor, where R’ is not of oharaoteristio 2 or 3. If \phi is a 3-Lie homomorphism of R onto R',then \phi must be either a homoinorpiiisin or the negative of an anti-homomorphism of R onto R'. Theorem. Suppose that R is an associatiye ring and $R'\ne {0}$ is a prime ring,where (R', +) does not contain elements of the period 2 or 3. If \phi is a 3-Lie homomorphism of R onto R',then \phi it either a homomorphism or the negative of an antihomomorpliism of R onto R'. Theorem. Suppose that R is an associative ring and (R, +) does not contain element of the period 2 or 3,R' is a prime ring. If \phi is a 3-Lie isomorpJlism of R onto R'。then \phi is either a isomorphism or the negative of an anti-isomorphism of R onto R'.  相似文献   

7.
Let S be an antinegative commutative semiring without zero divisors and M_n(S)be the semiring of all n×n matrices over S.For a linear operator L on M_n(S),we say that L strongly preserves nilpotent matrices in M_n(S)if for any A∈M_n(S),A is nilpotent if and only if L(A)is nilpotent.In this paper,the linear operators that strongly preserve nilpotent matrices over S are characterized.  相似文献   

8.
马晶  徐晓伟 《东北数学》2006,22(1):105-113
Let R be a prime ring with center Z and S (?) R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x-xG(x) ∈ Z for all x ∈ S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime case is also considered.  相似文献   

9.
Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving (scp) on S, if [f(x), f(y)] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.  相似文献   

10.
双边Prequantale中的Frame核映射   总被引:1,自引:1,他引:0  
In this paper, a Frame nucleus and prime elements in a Prequantale are defined. The concrete structure of a Frame prequantic quotient is considered, and the relation between the half-prime element and the Frame nucleus in a two-side Prequantale are obtained.  相似文献   

11.
Let R be a commutative ring with identity, Z(R) its set of zero-divisors, and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is Γ(R) = Z(R)\{0}, with distinct vertices x and y adjacent if and only if xy = 0. In this article, we study Γ(R) for rings R with nonzero zero-divisors which satisfy certain divisibility conditions between elements of R or comparability conditions between ideals or prime ideals of R. These rings include chained rings, rings R whose prime ideals contained in Z(R) are linearly ordered, and rings R such that {0} ≠ Nil(R) ? zR for all z ∈ Z(R)\Nil(R).  相似文献   

12.
A (commutative unital) ring R with only finitely many minimal prime ideals (for instance, a Noetherian ring) is reduced and a strong (A)-ring if and only if R is an integral domain. Thus, the smallest reduced ring which has Property A but is not a strong (A)-ring is ${\mathbb{Z}_{2} \times \mathbb{Z}_{2}}$ . A Noetherian ring R is a strong (A)-ring if and only if Ass R (R) has a unique maximal element.  相似文献   

13.
Let R be a commutative ring, let Z(R) be the set of all zero-divisors of R and Reg(R) = R\Z(R). The regular graph of R, denoted by G(R), is a graph with all elements of Reg(R) as the vertices, and two distinct vertices x, y ∈ Reg(R) are adjacent if and only if x+yZ(R). In this paper we show that if R is a commutative Noetherian ring and 2 ∈ Z(R), then the chromatic number and the clique number of G(R) are the same and they are 2 n , where n is the minimum number of prime ideals whose union is Z(R). Also, we prove that all trees that can occur as the regular graph of a ring have at most two vertices.  相似文献   

14.
The sumN(R) of nil one-sided ideals of bounded index of a ringR is shown to coincide with the set of all strongly nilpotent elements ofR of bounded index. The known result thatN(R) is contained in the prime radical is highly improved and it is shownN(R) is contained inN 2(R). It is proved that the sum of a finite number of nil left ideals of bounded index has bounded index.  相似文献   

15.
For a family A{\mathcal{A}} and a set Z, denote {A ? A \colon A ?Z 1 ?}{\{A \in \mathcal{A} \colon A \cap Z \neq \emptyset\}} by A(Z){\mathcal{A}(Z)}. For positive integers n and r, let Sn,r{\mathcal{S}_{n,r}} be the trivial compressed intersecting family {A ? (c[n]r ) \colon 1 ? A}{\{A \in \big(\begin{subarray}{c}[n]\\r \end{subarray}\big) \colon 1 \in A\}}, where [n] : = {1, ?, n}{[n] := \{1, \ldots, n\}} and (c[n]r ) : = {A ì [n] \colon |A| = r}{\big(\begin{subarray}{c}[n]\\r \end{subarray}\big) := \{A \subset [n] \colon |A| = r\}}. The following problem is considered: For rn/2, which sets Z í [n]{Z \subseteq [n]} have the property that |A(Z)| £ |Sn,r(Z)|{|\mathcal{A}(Z)| \leq |\mathcal{S}_{n,r}(Z)|} for any compressed intersecting family A ì (c[n]r ){\mathcal{A}\subset \big(\begin{subarray}{c}[n]\\r \end{subarray}\big)}? (The answer for the case 1 ? Z{1 \in Z} is given by the Erdős–Ko–Rado Theorem.) We give a complete answer for the case |Z| ≥ r and a partial answer for the much harder case |Z| < r. This paper is motivated by the observation that certain interesting results in extremal set theory can be proved by answering the question above for particular sets Z. Using our result for the special case when Z is the r-segment {2, ?, r+1}{\{2, \ldots, r+1\}}, we obtain new short proofs of two well-known Hilton–Milner theorems. At the other extreme end, by establishing that |A(Z)| £ |Sn,r(Z)|{|\mathcal{A}(Z)| \leq |\mathcal{S}_{n,r}(Z)|} when Z is a final segment, we provide a new short proof of a Holroyd–Talbot extension of the Erdős-Ko-Rado Theorem.  相似文献   

16.
In this paper we study the probability that the commutator of two randomly chosen elements in a finite group is equal to a given element of that group. Explicit computations are obtained for groups G which |G| is prime and GZ(G) as well as for groups G which |G| is prime and GZ(G)=1. This paper extends results of Rusin [see D.J. Rusin, What is the probability that two elements of a finite group commute? Pacific J. Math. 82 (1) (1979) 237-247].  相似文献   

17.
Hull-kernel topology on the set ∑(R) of prime ideals of a ring R with unity and without nilpotent elements is discussed. The restriction of this topology to the set π(R) of minimal prime ideals of R has been investigated in detail. The compactness of π(R) has been characterized in several ways. An interesting characterization of Baer rings is given.A functorial correspondence between the category of rings having the property that every prime ideal contains a unique minimal prime ideal and their minimal spectra is established.  相似文献   

18.
We introduce a class of infinite matrices (Ass, s, s¢ ? \mathbbZd){(A_{ss\prime}, s, s\prime \in \mathbb{Z}^d)} , which are asymptotically (as |s| + |s′| → ∞) close to Hankel–T?plitz matrices. We prove that this class forms an algebra, and that flow-maps of nonautonomous linear equations with coefficients from the class also belong to it.  相似文献   

19.
Suppose that K is a compact set in the open complex plane. In this paper, we prove an existence criterion for an estimate of Markov-Bernstein type for derivatives of a rational function R(z) at any fixed point z 0K. We prove that, for a fixed integer s, the estimate of the form |R (s) (z 0)| ≤ C(K, z 0, s)nR C(K), where R is an arbitrary rational function of degree n without poles on K and C is a bounded function depending on three arguments K, z 0, and s, holds if and only if the supremum $$\omega (K,z_0 ,s) = \sup \left\{ {\frac{{\operatorname{dist} (z,K)}}{{\left| {z - z_0 } \right|^{s + 1} }}} \right\}$$ over z in the complement of K is finite. Under this assumption, C is less than or equal to const ·s!ω(K, z 0, s).  相似文献   

20.
The commutators of oscillatory singular integral operators with homogeneous kernel \fracW(x)| x |n \frac{{\Omega (x)}}{{\left| x \right|^n }} are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).  相似文献   

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