منابع مشابه
Noetherian Modules
In a finite-dimensional vector space, every subspace is finite-dimensional and the dimension of a subspace is at most the dimension of the whole space. Unfortunately, the naive analogue of this for modules and submodules is wrong: (1) A submodule of a finitely generated module need not be finitely generated. (2) Even if a submodule of a finitely generated module is finitely generated, the minim...
متن کاملDo Noetherian Modules Have Noetherian Basis Functions?
In Bishop-style constructive algebra it is known that if a module over a commutative ring has a Noetherian basis function, then it is Noetherian. Using countable choice we prove the reverse implication for countable and strongly discrete modules. The Hilbert basis theorem for this specific class of Noetherian modules, and polynomials in a single variable, follows with Tennenbaum’s celebrated ve...
متن کاملModules with Noetherian second spectrum
Let $R$ be a commutative ring and let $M$ be an $R$-module. In this article, we introduce the concept of the Zariski socles of submodules of $M$ and investigate their properties. Also we study modules with Noetherian second spectrum and obtain some related results.
متن کاملNONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS
In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...
متن کاملQuotients of Standard Hilbert Modules
We initiate a study of Hilbert modules over the polynomial algebra A = C[z1, . . . , zd] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity version of one of these. Standard Hilbert modules occupy a position analogous to that of free modules of finite rank in commutative algebra, and their quot...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0277460-4