共查询到19条相似文献,搜索用时 27 毫秒
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本文研究了α-诣零Armendariz 环的性质. 利用环R 上的斜多项式环, 得到了α-诣零Armendariz 环的例子并研究了它的扩张, 推广了文献[4] 中关于诣零Armendariz 环的相应的结论. 相似文献
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本文研究了容有半对称度量联络的广义复空间中的子流形上的Chen-Ricci不等式.利用代数技巧,建立了子流形上的Chen-Ricci不等式.这些不等式给出了子流形的外在几何量-关于半对称联络的平均曲率与内在几何量-Ricci曲率及k-Ricci曲率之间的关系,推广了Mihai和Özgür的一些结果. 相似文献
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For a ring endomorphism α, we introduce and investigate SPA-rings which are a generalization of α-rigid rings and determine the radicals of the skew polynomial rings R[x; α], R[x, x ?1; α] and the skew power series rings R[[x; α]], R[[x, x ?1; α]], in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SPA-ring. We will construct various types of nonreduced SPA-rings and show SPA is a strictly stronger condition than α-rigid. 相似文献
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Let R be a ring, σ an injective endomorphism of R and δ a σ-derivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ,δ] and both rings have the same left uniform dimension.
Presented by S. Montgomery
Mathematics Subject Classification (2000) 16S90.
Jerzy Matczuk: Supported by the Flemish–Polish bilateral agreement BIL 01/31. 相似文献
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Michał Ziembowski 《代数通讯》2013,41(2):664-666
One of the main results of the article [2] says that, if a ring R is semiperfect and ? is an authomorphism of R, then the skew Laurent series ring R((x, ?)) is semiperfect. We will show that the above statement is not true. More precisely, we will show that, if the Laurent series ring R((x)) is semilocal, then R is semiperfect with nil Jacobson radical. 相似文献
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ZhongKuiLIU JavedAHSAN 《数学学报(英文版)》2004,20(1):105-114
Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U. 相似文献
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The Nagata ring R(X) and the Serre’s conjecture ring R?X? are two localizations of the polynomial ring R[X] at the polynomials of unit content and at the monic polynomials, respectively. In this paper, we contribute to the study of Prüfer conditions in R(X) and R?X?. In particular, we solve the four open questions posed by Glaz and Schwarz in Section 8 of their survey paper [38] related to the transfer of Prüfer conditions to these two constructions. 相似文献
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We introduce weak Armendariz rings which are a generalization of semicommutative rings and Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak Armendariz if and only if for any n, the n-by-n upper triangular matrix ring T n (R) is weak Armendariz. If R is semicommutative, then it is proven that the polynomial ring R[x] over R and the ring R[x]/(x n ), where (x n ) is the ideal generated by x n and n is a positive integer, are weak Armendariz. 相似文献
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A ring R with identity is called “clean” if every element of R is the sum of an idempotent and a unit, and R is called “strongly clean” if every element of R is the sum of an idempotent and a unit that commute. Strongly clean rings are “additive analogs” of strongly regular rings, where a ring R is strongly regular if every element of R is the product of an idempotent and a unit that commute. Strongly clean rings were introduced in Nicholson (1999) where their connection with strongly π-regular rings and hence to Fitting's Lemma were discussed. Local rings and strongly π-regular rings are all strongly clean. In this article, we identify new families of strongly clean rings through matrix rings and triangular matrix rings. For instance, it is proven that the 2 × 2 matrix ring over the ring of p-adic integers and the triangular matrix ring over a commutative semiperfect ring are all strongly clean. 相似文献