共查询到20条相似文献,搜索用时 15 毫秒
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M. B. Zwyagina 《Journal of Mathematical Sciences》2002,112(4):4337-4347
Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given. Let
be a Noetherian commutative ring, let
be a set of maximal ideals in
, and let
. Then the category of Artinian modules is dual to the category of Noetherian modules. Several structural results are proved, including the theorem on the structure of Artinian modules over principal ideal domains. For rings of special kinds, double centralizer theorems are proved. Bibliography: 5 titles. 相似文献
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Mathematische Annalen - 相似文献
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M. Davoudian 《代数通讯》2013,41(9):3907-3917
We introduce and study the concept of dual perfect dimension which is a Krull-like dimension extension of the concept of acc on finitely generated submodules. We observe some basic facts for modules with this dimension, which are similar to the basic properties of modules with Noetherian dimension. For Artinian serial modules, we show that these two dimensions coincide. Consequently, we prove that the Noetherian dimension of non-Noetherian Artinian serial modules over the rings of the title is 1. 相似文献
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在[1]文中利用极大左理想刻画了Noether环,本文引进Noether左理想、Artin左理想、m左理想等概念(当I是环R的极大左理想时, I既是Noether、Artin的也是m的,此时m=1。),证明了[1]文中相应的结论,给出了相应的Artin环的刻画。 定义1 环R的左理想I称为Artin(Noether),如果R/I是Artin(Noether)R模。 定义2 环R的左理想I称为m理想,如果R/I的任何R子模都可由m个元生成。 本文的主要结论: 相似文献
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Gary Brookfield 《Semigroup Forum》2003,66(2):323-327
We provide a short proof that a commutative semigroup is finitely generated if its lattice of congruences is Noetherian. 相似文献
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Brookfield 《Semigroup Forum》2008,66(2):323-327
Abstract. We provide a short proof that a commutative semigroup is finitely generated if its lattice of congruences is Noetherian. 相似文献
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It is well known that every serial Noetherian ring satisfies the restricted minimum condition. In particular, following Warfield (1975), such a ring is a direct sum of an Artinian ring and hereditary prime rings. The aim of this note is to show that every serial ring having the restricted minimum condition is Noetherian. 相似文献
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众所周知,环R是右Noether的当且仅当任意内射右R-模的直和是内射的.本文我们将用Ne-内射模和U-内射模来刻画Ne-Noether环和U-Noether环. 相似文献
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Let G be a torsion group and R be a commutative ring with identity. We investigate reversible group rings RG over commutative rings, extending results of Gutan and Kisielewicz which characterize all reversible group rings over fields. 相似文献
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《Finite Fields and Their Applications》2001,7(3):382-396
A commutative ring with identity is called a chain ring if all its ideals form a chain under inclusion. A finite chain ring, roughly speaking, is an extension over a Galois ring of characteristic pnusing an Eisenstein polynomial of degree k. When p∤k, such rings were classified up to isomorphism by Clark and Liang. However, relatively little is known about finite chain rings when p∣k. In this paper, we allowed p∣k. When n=2 or when p∥k but (p−1)∤k, we classified all pure finite chain rings up to isomorphism. Under the assumption that (p−1)∤k, we also determined the structures of groups of units of all finite chain rings. 相似文献
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Wolfgang Rump 《Algebras and Representation Theory》2006,9(3):227-239
We introduce and study lattice-finite Noetherian rings and show that they form a onedimensional analogue of representation-finite Artinian rings. We prove that every lattice-finite Noetherian ring R has Krull dimension ≼ 1, and that R modulo its Artinian radical is an order in a semi-simple ring. Our main result states that maximal overorders of R exist and have to be Asano orders, while they need not be fully bounded. This will be achieved by means of an idempotent ideal I(R), an invariant or R which is new even for classical orders R. This ideal satisfies I(R) = R whenever R is maximal.
Presented by H. Tachikawa 相似文献
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François Couchot 《代数通讯》2013,41(2):346-351
Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring 𝕄 n (R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is a valuation ring. It is also shown that each R-algebra which is locally a direct limit of module-finite algebras, is strongly clean if R is a π-regular commutative ring. 相似文献
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Mikhail A. Chebotar 《代数通讯》2013,41(12):4339-4344
Let R be a 2-torsion free commutative ring with identity, and δ a nonzero derivation of R such that R is δ-prime. Then Rδ is a prime Lie ring and any nonzero ideal of Rδ contains an ideal of the form Jδ where J is a nonzero δ-ideal of R. 相似文献
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本文利用局部化的方法,由Artin环上加性秩函数的分解形式决定了Noether环上所有加性秩函数的形式(与[1]相同),且在同一模范畴中刻画了原子秩函数的意义,得出一新的结论. 相似文献
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