PRIME AND MAXIMAL IDEALS IN CONSTRUCTIVE RING THEORY

The basic notions of ideal theory are examined constructively in the context of a commutative ring with an identity and an inequality relation. Constructive analogues of classical theorems relating maximality and primeness are proved, and it is shown that the results are the best possible in a constructive framework.     

软代数的素理想与同余关系

本文用软代数的素理想集刻划了软代数的每一个同余关系，并给出了软代数的同余理想用素理想集刻划的表达式。     

DIMENSIONS OF THE RING OF INVARIANT OPERATORS ON BOUNDED HOMOGENEOUS DOMAINS

Let \[{\cal D}\] be the bounded homogeneous domain, \[G({\cal D})\]be the group of the auto- morphism of \[{\cal D}\]. A differential operator T of (k,l) type is called invariant, if and only if it is commutative with the actions of the \[G({\cal D})\] . The ring of the (k,l) type invariant differential operators is denoted by \[{I_{k,l}}({\cal D})\]. This paper gives a formula for caculating the dimension of \[{I_{k,l}}({\cal D})\]. Obviously, these dimensions are the invarians of \[{\cal D}\] in analytical equivalence, By means 〇f the results in the famous work of A,, Selberg⁴, and applying the theory of group representations, we have proved the following Theorem. \[\dim {I_{k,l}}({\cal D})/\sum\limits_{({k^'},{l^'}) < (k,l)} {{I_{{k^'},{l^'}}}({\cal D})} = \int_K^{} {\cal X} (k,0,...,0)(A)\overline {{\cal X}(k,0,...,0)(A)} \dot A\]K where K is the group formed by the linear parts of the isotropy of \[G({\cal D})\] at \[0 \in {\cal D}\] and \[{{\cal X}(k,0,...,0)(A)}\] is the character of the irreducible representation of the unitary group U(n) with Young index (k, 0, ???, 0). Using this formula, we caculate the dimensions for some concrete cases, including those with the classical symmetric domain, and with a Siegel domain that is not symmetric.     

一个特征标环素谱的连通性

本文确定了一个有限群特征标环通过代数整数环扩张后素谱的结构，在此基础之上，利用与[1]中类似的方法证明了这个扩张后的特征标环素谱的连通性。同时还计算了有限群的复类函数空间的幂等元．     

ON WEIGHT MODULES OF ALGEBRAS OF TWISTED DIFFERENTIAL OPERATORS ON THE PROJECTIVE SPACE

We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on ? ⁿ . Necessary and sufficient conditions for these blocks to be tame and proofs that some of the blocks are Koszul are provided. We also establish equivalences of categories between these blocks and categories of bounded and generalized bounded weight Open image in new window -modules in the cases of nonintegral and singular central character.     

ON SELF-ADJOINTNESS OF THE PRODUCT OF TWO n-ORDER DIFFERENTIAL OPERATORS ON[a,b]

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅｗｅｒｅｍａｎｙａｒｔｉｃｌｅｓｏｎｔｈｅｐｒｏｄｕｃｔｓｏｒｐｏｗｅｒｓｏｆｄｉｆｅｒｅｎｔｉａｌｏｐｅｒａｔｏｒｓ，ｅｓｐｅｃｉａｌｙｏｎｄｅｆｉｃｉｅｎｃｙｉｎｄｉｃｅｓｏｆｔｈｅｐｏｗｅｒｓｏｆｄｉｆｅｒｅ...     

ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC^{\perp}ON ANNIHILATOR IDEALS.

The author concludes that every commutative ring with ascending chain condition an annihilator ideals has a Kasch quotient ring, which generalizes the Theorem^{[1]} that every commutative noetherian ring has a Kasch quosient ring. If follows that if R is a commutative ting with acc^{\perp}，then that Q(R) is semiprimary is equivalent to that it is perfect, or to that R satisfies regular condition. Besides, that Q(R) is quasi-frobenius equals that Q(R) is FPF or PF, and that Q(R) is artinian equals that R/N, are of finite dimension, i=1,2,\ldots,n. N_{i}=J^{i}\cap R.     

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...     

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.     

一类具指数系数的对称微分算子的谱及亏指数

就一类具指数函数系数的高阶对称微分算子得到了谱是离散的一些充分条件,并给出了完全可达的亏指数域.     

ON J-SELFADJOINT EXTENSION OF THE PRODUCT OF TWO nTH-ORDER J-SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS ON [a,b]

The problem of J-selfadjointness of the product of two nth-order J-symmetric operators on [a,b] is studied. We give a condition to ensure that the product operator is a J-selfadjoint extension.     

算子变形的一种方法

本文提出算子的一种变形方法,可以改善算子的逼近度.§1叙述这种变形的方法,§2讨论它的某些应用.§1.算子变形的一种方法C~n[α,b]表示区间[α,b]上具有 n 阶连续导数的函数类,用 C[α,b]表示[α,b]上的连续函数全体.有线性算子     

ON THE FUNCTIONAL-DIFFERENTIAL EQUATION OF THE DISTRIBUTION OF PRIME NUMBERS

1IntroductionsandStatementsInt-,iloIf)4-0'sCllorw'3I](see(ieVisme[4],Wright[:l]alldDriver[1])al,t}(}Inr)1,cdforil](lal[(lllrisl-,i(ital]yarlalyti(:itlI)rooftilt)prim(?number1,if(3or'3m5whi相似文献   

ON THE NORMALITY OF MONOMIAL IDEALS OF MIXED PRODUCTS

Let R = K[x, y] be a polynomial ring in two disjoint sets of variables x, y over a field K. We study ideals of mixed products L = I_kJ_r + I_sJ_t such that k + r = s + t, where I_k (resp. J_r ) denotes the ideal of R generated by the square-free monomials of degree k (resp. r) in the x (resp. y ) variables. Our main result is a characterization of when a given ideal L of mixed products is normal.

     

关于算子正矩阵

关于算子正矩阵侯晋川，高明杵（山西师范大学数学系，临汾０４１００４）基金项目：国家自然科学基金、山西省自然科学基金资助课题１９９２年３月１９日收到．由于应用的广泛性，人们对于寻求块方阵（）为半正定矩阵的（充分或必要）条件一直很感兴趣，且已获得许多深刻...     

DIFFERENTIAL OPERATORS OF INFINITE ORDER IN THE SPACE OF RAPIDLY DECREASING SEQUENCES

We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it.The object of this article is to study the equivalence of a differential operator of infinite order;that is φ(D) =sum from k=0 to ∞φ_κD~κ.φ_κ constant numbers an a power of D.D~n,meaning,is there a isomorphism X(from s onto s) such that X_φ(D) = D~nX?.We prove that if φ(D) is equivalent to D~n,then φ(D) is of finite order,in fact a polynomial of degree n.The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n=1.     

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

1.IntroductionInwhatfollows,allofHilbertspacesappearedinthispaperareinfinite-dimensionalseparablecomplexHilbertspace.IfHisaHilbertspace,thenC(n)denotestheC*--algebraofallboundedlinearoperatorsonHandK(H)denotesthesetofcompactoperatorsonn.TwooperatorsSandTarecalledapproximatelyequivalentifthereisasequenc{Un}ofunitaryoperatorssuchthatlIU:SUn--Tll-0(n-- co).SimilarlytwooperatosSandTareapproximatelysimilarifthereisasequence{Vn}ofinvertibleoperatorswithsup(llVn11,11VJ'11)相似文献