关于素环的导子

设Ｒ是一个中心为Ｃ的素环，Ｎ是Ｒ的一个非零理想。本文我们将证明下列结果：假设ｄ是Ｒ的一个非零导子使得ｄ＾２（ａ＾２）∈Ｃ对一切ａ∈Ｎ或者〔ｄ（ａ），ａ＾２〕∈Ｃ对一切ａ∈Ｎ，那么当Ｒ的特征不等于２时，Ｒ是一个交换环。我们的结果推广了文献〔２，〔４〕，〔８〕中有关素环导子的某些已知结果。     

Conditions on Normal Spaces of Finite Rank That Guarantee C(X) is SV

An f-ring A is an SV f-ring if for every minimal prime ?-ideal P of A, A/P is a valuation domain. A topological space X is an SV space if C(X) is an SV f-ring. For normal spaces, several conditions are shown to guarantee the space is an SV space. For example, a normal space of finite rank for which the closure of the set of points of rank greater than 1 is an F-subspace, is an SV space. For normal spaces of rank 2, a characterization of SV spaces is given.     

ON CERTAIN SUBGROUPS OF PRIME RINGS WITH DERIVATIONS

Let R be a noncommutative prime ring and let d be a nonzero derivation on R. A classical theorem of Posner asserts that the subset {[x ^d , x]|x ∈ R} is not contained in the center of R. Under the additional assumption that char R ≠ 2 and d ³ ≠ 0, we show that the additive subgroup of R generated by the subset {[x ^d , x] | x ∈ R} contains a noncentral Lie ideal of R.     

Images and Open Subspaces of SV Spaces

A topological space is finitely an F-space if its Stone–?ech compactification is a union of finitely many closed F-spaces and a space is SV if C(X) has the property that C(X)/P is a valuation domain for each prime ring ideal P of C(X). This article studies the images under open continuous functions and the open subspaces of spaces that are finitely an F-space or are SV. It is shown that an open continuous image of a compact space that is finitely an F-space is finitely an F-space and an open continuous image of certain SV spaces is SV. Also, it is shown cozerosets, but not necessarily open sets, of SV spaces are SV spaces and a similar situation holds for spaces that are finitely an F-space.     

Hopf余模代数Smash积的理想

Ｈｏｐｆ余模代数Ｓｍａｓｈ积的理想陈惠香（扬州大学师范学院，扬州２２５００２）本文恒设Ｈ是域ｋ上Ｈｏｐｆ代数，Ｓ为Ｈ的ａｎｔｉｐｏｄｅ，Ｈ“为Ｈ的对偶代数。如果Ｓ是双射，则用工表示Ｓ的逆映射．有关记号参阅文ｏｆ］．设Ａ是右Ｈ一余模代数．则自然嵌人Ａ①...     

There do not exist minimal algebras between C*(X) and C(X) with prescribed real maximal ideal spaces

Let C(X) be the algebra of all real-valued continuous functions on a completely regular Hausdorff space X, and C*(X) the subalgebra of bounded functions. We prove that for any intermediate algebra A between C*(X) and C(X), other than C*(X), there exists a smaller intermediate algebra with the same real maximal ideals as in A. The space X is called A-compact if any real maximal ideal in A corresponds to a point in X. It follows that, for a noncompact space X, there does not exist any minimal intermediate algebra A for which A is A-compact. This completes the answer to a question raised by Redlin and Watson in 1987.     

PRIME IDEALS IN RINGS WITH INVOLUTION

Abstract

Let R be a ring with involution *. We show that if R is a *-prime ring which is not a prime ring, then R is “essentially” a direct product of two prime rings. Moreover, if P is a *-prime *-ideal of R, which is not a prime ideal of R, and X is minimal among prime ideals of R containing P, then P is a prime ideal of X, P = X ∩ X* and either: (1) P is essential in X and X is essential in R; or (2) for any relative complement C of P in X, then C* is a relative complement of X in R. Further characterizations of *-primeness are provided.     

When Min(A)−1 is Hausdorff

For a commutative ring with identity, say A, its collection of minimal prime ideals is denoted by Min(A). The hull-kernel topology on Min(A) is a well-studied structure. For example, it is known that the hull-kernel topology on Min(A) has a base of clopen subsets, and classifications of when Min(A) is compact abound. Recently, a program of studying the inverse topology on Min(A) has begun. This article adds to the growing literature. In particular, we characterize when Min(A)^?1 is Hausdorff. In the final section, we consider rings of continuous functions and supply examples.     

On a class of subalgebras of and the intersection of their free maximal ideals

Let be a Tychonoff space and a subalgebra of containing . Suppose that is the set of all functions in with compact support. Kohls has shown that is precisely the intersection of all the free ideals in or in . In this paper we have proved the validity of this result for the algebra . Gillman and Jerison have proved that for a realcompact space , is the intersection of all the free maximal ideals in . In this paper we have proved that this result does not hold for the algebra , in general. However we have furnished a characterisation of the elements that belong to all the free maximal ideals in . The paper terminates by showing that for any realcompact space , there exists in some sense a minimal algebra for which becomes -compact. This answers a question raised by Redlin and Watson in 1987. But it is still unsettled whether such a minimal algebra exists with respect to set inclusion.

     

Algebras between C *(X) and C(X) that are closed under countable composition

Let be the algebra of all real-valued continuous functions on a completely regular space X, and the subalgebra of bounded functions. We show that the space of real maximal ideals of an intermediate algebra between and is a -embedded closed subspace of the product of with a product of copies of the real line. We make use of this embedding to provide a new characterization of the intermediate algebras that are closed under countable composition, and to exhibit an example of an intermediate algebra on that is closed under countable composition but not isomorphic to any .     

ON A CLASSIFICATION OF PRIME RINGS

Abstract

We formalize the adjunction of maps of localized nilpotent spaces of the homotopy type of CW-complexes. Using the semilocalization theory of M. Bendersky, in which only the higher homotopy groups are localized, we obtain an adjunction theorem with fewer nilpotency conditions on the spaces. The two main theorems are in the form of a theorem on maps of triads by J. P. May.     

STABILITY OF CERTAIN RINGS OF HIGHEST WEIGHT VECTORS

51. IntroductionLet Cm'" be the space of complex m x n matrices, P(Cm)") be the algebra of complexpolynomials on Cd'~. Let GLm(C) x GL.(C) act on P(Cm,") as the following:(gi, gZ)f(x) ~ f(g,'xg,),where x E Cat", (gi, g2) E GLm x GL., f E P(Cm'"). This action induces an action of thesubgroup Of x GL. on P(Cm)") by restriction.Let G be a complex reductive algebraic group, (V, p) be a rational representation of G.Let B = TU be a Borel subgroup of G, where T is a majximal torns of …     

有限群中素数方幂阶子群的个数

本文利用基础代数中有关稳定子、陪集等理论,给出了有限群G中pk阶子群个数的 一个结果.     

ON SOME SPECIAL CLASSES OF PRIME RINGS

Abstract

Given a non-zero cardinal α, a ring R is said to be SP(α) if a is the first cardinal for which every non-zero element of R has an insulator of cardinality less than α + 1.

It is shown that the class of SP(α) rings is a special class (in the sense of Andrunakievi?) for each α. A theorem of Groenewald and Heyman (also Desale and Varadarajan) to the effect that the class of all strongly prime rings is a special class is obtained as a corollary. Every SP(α) ring has an SP(α) rational extension ring with identity.     

环上的σ-导子

本文研究了σ－导子的扩张问题，并且在本原环上刻化了s－导子。     

ASYMPTOTIC PROPERTIES OF ELEMENTS IN GROUP RINGS OF FINITE GROUPS

A relation between algebraic degrees of eigenvalues of an element in the group ring Z G of a finite group G and their multiplicities is obtained. This result can be regarded as a theorem on asymptotic behavior of parameters in group rings of finite groups which is a parallel result of several well known theorems concerning the relationships of parameters in finite groups.     

THE RANGES OF ADDITIVE MAPS IN GENERALIZED FUNCTIONAL IDENTITIES ON PRIME RINGS

ABSTRACT

In the present paper we prove that a conjecture proposed by Bre?ar is true. According to Chebotar's result we generalize the conjecture.     

ON THE COMMUTATIVITY OF PRIME RINGS WITH DERIVATION

Abstract

We study commutativity of prime rings R such that d(S) is central, where d is a non-zero derivation and S a suitably-chosen subset of R.     

有限环上r-MDR码与r-MDS码

本文研究了有限环上r-MDR码与r-MDS码.利用主理想环CRT（R₁,R₂,…,R_s）上的r-MDR码或P_r-MDS码CRT（C₁,C₂,…,C_s）,得到了某个链环R_i上的码C_i也是r-MDR码或P_r-MDR码.特别地,对于有限链环上的码C,给出了它的挠码Tor_i（C）为r-MDR码与r-MDS码的条件.