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1.
Contractedness of 𝔪-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, 𝔪). In such rings, the contracted 𝔪-primary ideals are known to be characterized by the property that I: 𝔪 = I: x for some x ∈ 𝔪 ?𝔪2. We call the ideals with this property full ideals and compare this class of ideals with the classes of 𝔪-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The 𝔪-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be 𝔪-full. We also show the equivalence of the properties full, 𝔪-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full. 相似文献
2.
Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented. 相似文献
3.
GL_2 OVER FULL RINGS 总被引:1,自引:1,他引:0
In this paper the authors generalize the result of B.R.McDonald.The following resultis obtained.Let R be a(1,6)-full ring,or(3,3)-full ring,or(2,4)-full ring,and R has theproperty T.G is an SL_2(R)-normal subgroup of GL_2(R).Then there is an ideal A in Rsuch thatSC(R,A)(?)G(?)GC(R,A). 相似文献
4.
In this paper,let m,n be two fixed positive integers and M be a right R-module,we define (m,n)-M-flat modules and (m,n)-coherent modules.A right R-module F is called (m,n) M-flat if every homomorphism from an (n,m)-presented right R-module into F factors through a module in addM.A left S-module M is called an (m,n)-coherent module if MR is finitely presented,and for any (n,m)-presented right R-module K,Horn(K,M) is a finitely generated left S-module,where S = End(MR).We mainly characterize (m,n)-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules.Some properties of (m,n)-coherent rings and coherent rings are obtained as corollaries. 相似文献
5.
In this paper, let m, n be two fixed positive integers and M be a right R-module, we define (m, n)-M-flat modules and (m, n)-coherent modules. A right R-module F is called (m, n)-M-flat if every homomorphism from an (n, m)-presented right R-module into F factors through a module in addM. A left S-module M is called an (m, n)-coherent module if MR is finitely presented, and for any (n, m)-presented right R-module K, Hom(K, M) is a finitely generated left S-module, where S = End(MR). We mainly characterize (m, n)-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules. Some properties of (m, n)-coherent rings and coherent rings are obtained as corollaries. 相似文献
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7.
张隆辉 《数学的实践与认识》2013,43(6)
证明了一类n阶(n=P_1P_2…p_m,p_i(i=1,2,…,m)互异为素数)环是有限循环环,并讨论了他们的结构及相关性质,最后给出了这类n阶环有零因子或有子域的充要条件.主要结果:P_1P_2…P_m阶环共有2m个,它们是(p_(1m个,它们是(p_(1k_1) p_(2k_1) p_(2k_2)…p_(mk_2)…p_(mk_m)Z)/(p_(1k_m)Z)/(p_(1k_1+1)p_(2k_1+1)p_(2k_2+1)…p_(mk_2+1)…p_(mk_m+1)Z),其中k_i=0或1,1≤i≤m;阶是n=P_1P_2…p_m的环R可唯一分解为m个素数阶理想的直和,即R=〈α〉=(?);含pi(1≤i≤m)阶子域的P_1P_2…P_m阶环共有2k_m+1)Z),其中k_i=0或1,1≤i≤m;阶是n=P_1P_2…p_m的环R可唯一分解为m个素数阶理想的直和,即R=〈α〉=(?);含pi(1≤i≤m)阶子域的P_1P_2…P_m阶环共有2(m-1)个,它们是p_(1(m-1)个,它们是p_(1k_1) p_(2k_1) p_(2k_2)…p_(mk_2)…p_(mk_m)Z)/(p_(1k_m)Z)/(p_(1k_1+1)p_(2k_1+1)p_(2k_2+1)…p_(mk_2+1)…p_(mk_m+1)Z),其.中k_i=0,k_j=0或1,1≤j≤m,j≠i. 相似文献
8.
Salles Danielle 《代数通讯》2013,41(5):923-940
For every (n,m) ? IN?× IN ?, verifying l We study direct systems of rings and give a bound for the pure - global - dimension of their limits, not depending on the ring cardinality. Using this result and a theorem of C0UCH0T we give examples of pure -heriditary group- rings (ie. of pure -global - dimension one) of large cardinality. Finaly we prove - using a result of VASC0NCEL0S and a theorem of JENSEN - that some countably products of noetherian rings are coherent rings and that their pure - global - dimension is exactly two. 相似文献
9.
STABILITY OF CERTAIN RINGS OF HIGHEST WEIGHT VECTORS 总被引:1,自引:0,他引:1
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 … 相似文献
10.
设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A~2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n0且m≠n时,每一个从R到M的(m,n)-Jordan导子恒等于零.还证明了,如果A和B是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n0且m≠n,U=[A N M B]是一个|mn(m-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零. 相似文献
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Juan Migliore Rosa M. Miró-Roig Satoshi Murai Uwe Nagel Junzo Watanabe 《Archiv der Mathematik》2013,101(5):445-454
A homogeneous ideal I of a polynomial ring S is said to have the Rees property if, for any homogeneous ideal ${J \subset S}$ which contains I, the number of generators of J is smaller than or equal to that of I. A homogeneous ideal ${I \subset S}$ is said to be ${\mathfrak{m}}$ -full if ${\mathfrak{m}I:y=I}$ for some ${y \in \mathfrak{m}}$ , where ${\mathfrak{m}}$ is the graded maximal ideal of ${S}$ . It was proved by one of the authors that ${\mathfrak{m}}$ -full ideals have the Rees property and that the converse holds in a polynomial ring with two variables. In this note, we give examples of ideals which have the Rees property but are not ${\mathfrak{m}}$ -full in a polynomial ring with more than two variables. To prove this result, we also show that every Artinian monomial almost complete intersection in three variables has the Sperner property. 相似文献
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14.
R. Seibold E. Krätzel 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1998,68(1):305-320
Zusammenfassung We consider the distribution ofk-full numbers. But we go into more detail and investigate suchk-full integers which are at the same timel-free. We give asymptotic results for the numberN
k,l (x) ofk- full andl-free integers not exceedingx in cases ofl =k + r with 2 ≤r ≤ 5. Moreover, we consider these cases and the casesk = 2, 3,l ≥k + 2 also under the assumption of Riemann’s Hypothesis.
相似文献
15.
It is proved that for matrices A,B in the n by n upper triangular matrix ring Tn(R) over a domain R,if AB is nonzero and central in Tn(R) then AB =BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties. 相似文献
16.
We study the distribution of r-full and l-free numbers in short intervals () and sharpen Kr?tzel’s and Wu’s results.
(Received 22 June 1999; in revised form 4 October 1999) 相似文献
17.
Manuel Saorin 《代数通讯》2013,41(14):5383-5394
It is obvious that OF and Von Neumann regular rings have monomorphic flat envelopes. In this paper we completely describe the structure,in terms of OF and Von Neumann regular rings, of those commutative rings all of whose modules have a monomorphic flat envelope (m.f.e. ). For that, we introduce the notion of locally QF ring with m.f.e., whose structure is given in terms of OF rings. It turns out that a commutative ring R with m.f.e. is characterized as a (essential) subdirect product of a locally QF ring with m.f.e. and a Von Neumann regular ring, with the latter flat as an R-module. 相似文献
18.
(MDS)- and Laguerre codes are closely related to geometry and can be used in order to construct certain finite incidence structures. Here we present some structure theorems on near rings, introduce the notion of a coding set of a near ring, which enables us to construct (MDS)-codes, and discuss the same problem for Laguerre codes. To find non trivial Laguerre sets in a near ring is much more difficult.Dedicated to Giuseppe Tallini on the occasion of his 60 th birthday 相似文献
19.
O. Chein E. G. Goodaire 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2005,75(1):245-255
In [5, 6], the second author and D. A. ROBINSON initiated a study of non-Moufang Bol loops with the property that over a field,
necessarily of characteristic 2, their loop rings satisfy the right, but not the left, Bol identity. They called such loops
SRAR and showed that the family of SRAR loops includes those Bol loops which have a unique non-identity commutator/associator.
In [4, 2], the current authors presented a construction for a new class of Bol loops denoted L(B,m,n,r,s,t,z,w) with initial
data a given (possibly associative) Bol loop B, elements, r, s, t, z and w in the centre of B, and integers m and n. 相似文献