共查询到18条相似文献,搜索用时 312 毫秒
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在此文中,我们对Strong-Armendariz环和Baer PP及PS环Ore-扩张R[x,x~(-1);α]的一些性质进行了讨论研究,并得到了一些结果.主要证明了R是Baer(PP)环当且仅当R[[x]]是Baer(PP)环及R是α-rigid环时,R是Baer(PP,PS)环当且仅当R[[x]]是Baer(PP,PS)环. 相似文献
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分次Armendariz环与P.P.环 总被引:1,自引:0,他引:1
引进分次Armendariz环的概念,讨论了分次环R= n∈2Rn及由它导出的非分次环R,R0,及R[x]之间关于Armendariz环性质的关系,并推广了[8]的结论,得到在R= n∈ZRn是Z-型正分次环的前提下,若R是分次Armendariz,分次正规环,则R是P.P环(Bear环)当且仅当R是分次P.P.环(分环Baer环)。 相似文献
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本文中我们引进强几乎优越扩张的概念并证明了若S≥R是(强几乎)优越扩张,则S是右Ⅱ-凝聚环当且仅当R是右Ⅱ-凝聚环。 相似文献
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Malcev-Neumann环的主拟Baer性质 总被引:2,自引:0,他引:2
设R是环,G是偏序群,σ是从G到R的自同构群的映射。本文研究了Malcev-Neumann环R*((G))是主拟Baer环的条件。证明了如下结果:如果R是约化环并且σ是弱刚性的,则R*((G))是主拟Baer环当且仅当R是主拟Baer环,并且I(R)的任意G可标子集在I(R)中具有广义并. 相似文献
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J-semicommutative环的性质 总被引:1,自引:0,他引:1
环冗称为J—semicommutative若对任意B,b∈R由ab=0可以推得aRb∈J(R),这里J(R)是环R的Jacobson根.环R是J—semicommutative环当且仅当它的平凡扩张是J—semicommutative环当且仅当它的Don'oh扩张是J—semicommutative环当且仅当它的Nagata扩张是,一semicommutative环当且仅当它的幂级数环是J—semicommutative环.若R/J(R)是semicommutative环,则可得到R是J-semicommutative环.本文进一步论证了如果,是环月的一个幂零理想,且R/I是J—semicommutative环,则R也是J-semicommutative环最后给出了J—semicommutative环与其他一些常见环的联系 相似文献
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定义了环R上的块循环矩阵环A,主要证明了下列结论:(1)若J是A的理想,d1,d2,…,dn是R的可逆元,则存在R的理想I使得J=I[σ1,σ2,…,σn].(2)若d1,d2,…,dn是R的可逆元,则(i)R是单环当且仅当A是单环;(ii)R是局部环当且仅当A是局部环;(iii)J(A)=J(R)[σ1,σ2,…,σn];(iv)R是半本原环当且仅当A是半本原环.(3)若d1,d2,…,dn都是R的幂零元,则J(A)=J(R) ( (i1,i2,…,im)∈r\(0,0,….0n)}RO2 2^1 O2 2^3…O2 2^3.(4)R是左Artin(Noether)环当且仅当A是左Artin(Noether)环.(5)若R有左Morita对偶(自对偶),则A有左Morita对偶(自对偶). 相似文献
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为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x~(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环. 相似文献
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Morita对偶和Smash积 总被引:1,自引:1,他引:0
设G是有限群,e为G的单位元,R=是有单位元的G-型分次环,T=R_e,R_U是极小内射余生成子.本文中,我们证明了R有左Morita对偶当且仅当Smash积R#G有左Morita对偶.设H是G的(正规)子群,若R有左Morita对偶,则R~((H))#H(R_((G/H))#(G/H))有左Morita对偶。当R是强分次环时,T有左Morita对偶当且仅当R有左Morita对偶当且仅当R#G有左Morita对偶. 相似文献
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Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xnR[x] is ideal-symmetric over a semiprime ring R. 相似文献
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如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环. 相似文献
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This article concerns a ring property called pseudo-reduced-over-center that is satisfied by free algebras over commutative reduced rings.The properties of radicals of pseudo-reduced-over-center rings are investigated,especially related to polynomial rings.It is proved that for pseudo-reduced-over-center rings of nonzero characteristic,the centers and the pseudo-reduced-over-center property are preserved through factor rings modulo nil ideals.For a locally finite ring R,it is proved that if R is pseudo-reduced-over-center,then R is commutative and R/J(R) is a commutative regular ring with J(R) nil,where J(R) is the Jacobson radical of R. 相似文献
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In this article we present some results about bounded factorization rings (BFRs), i.e., commutative rings with the property that each nonzero nonunit has a bound on the length of its factorizations into nonunits. In their article Factorization in Commutative Rings with Zero Divisors, Anderson and Valdes-Leon conjectured that R[x], the polynomial ring over R, is a bounded factorization ring if and only if R is a BFR and 0 is primary in R. We give some conditions under which the conjecture is true and present a bounded factorization ring with 0 primary where the polynomial ring is not a BFR. 相似文献
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In this article we investigate the transfer of the notions of elementary divisor ring, Hermite ring, Bezout ring, and arithmetical ring to trivial ring extensions of commutative rings by modules. Namely, we prove that the trivial ring extension R: = A ? B defined by extension of integral domains is an elementary divisor ring if and only if A is an elementary divisor ring and B = qf(A); and R is an Hermite ring if and only if R is a Bezout ring if and only if A is a Bezout domain and qf(A) = B. We provide necessary and sufficient conditions for R = A ? E to be an arithmetical ring when E is a nontorsion or a finitely generated A ? module. As an immediate consequences, we show that A ? A is an arithmetical ring if and only if A is a von Neumann regular ring, and A ? Q(A) is an arithmetical ring if and only if A is a semihereditary ring. 相似文献
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A *-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil *-clean rings are the *-version of nil-clean rings introduced by Diesl.This paper is about the nil *-clean property of rings with emphasis on matrix rings.We show that a *-ring R is nil *-clean if and only if J(R) is nil and R/J(R) is nil*-clean.For a 2-primal *-ring R,with the induced involution given by (aij)* =(a*ij)T,the nil *-clean property of Mn(R) is completely reduced to that of Mn(Z2).Consequently,Mn(R) is not a nil *-clean ring for n =3,4,and M2(R) is a nil *-clean ring if and only if J(R) is nil,R/J(R) is a Boolean ring and a*-a ∈ J(R) for all a ∈ R. 相似文献