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NOETHERIAN MODULES
"... In a finitedimensional vector space, every subspace is finitedimensional 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 ..."
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In a finitedimensional vector space, every subspace is finitedimensional 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.
ON NOETHERIAN CLASSES
"... Abstract. Let I (α) ≤ a. It was Taylor–Cavalieri who first asked whether hulls can be computed. We show that s  −3 = 0 −1. Is it possible to construct hulls? U. Newton [11] improved upon the results of V. Wang by extending hypernonnegative domains. 1. ..."
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Abstract. Let I (α) ≤ a. It was Taylor–Cavalieri who first asked whether hulls can be computed. We show that s  −3 = 0 −1. Is it possible to construct hulls? U. Newton [11] improved upon the results of V. Wang by extending hypernonnegative domains. 1.
ON THE NOTION OF COHENMACAULAYNESS FOR NON NOETHERIAN RINGS
, 809
"... ABSTRACT. There exist many characterizations of Noetherian CohenMacaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non Noetherian cas ..."
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case. Toward solving a conjecture posed by Glaz, we give a generalization of the HochsterEagon result on CohenMacaulayness of invariant rings, in the context of non Noetherian rings. 1.
Do Noetherian Modules Have Noetherian Basis Functions?
"... Abstract. In Bishopstyle 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 ..."
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Abstract. In Bishopstyle 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
The length of Noetherian modules
 Comm. Algebra
"... Abstract. We define an ordinal valued length for Noetherian modules which extends the usual definition of composition series length for finite length modules. Though originally defined by Gulliksen [1] in the 1970s, this extension has been seldom used in subsequent research. Despite this neglect, w ..."
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Abstract. We define an ordinal valued length for Noetherian modules which extends the usual definition of composition series length for finite length modules. Though originally defined by Gulliksen [1] in the 1970s, this extension has been seldom used in subsequent research. Despite this neglect
Multiplicity Of A Noetherian Intersection
, 1997
"... . A di#erential ring of analytic functions in several complex variables is called a ring of Noetherian functions if it is finitely generated as a ring and contains the ring of all polynomials. In this paper, we give an e#ective bound on the multiplicity of an isolated solution of a system of n equat ..."
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equations f i =0wheref i belong to a ring of Noetherian functions in n complex variables. In the onedimensional case, such an estimate is known and has applications in number theory and control theory. Multidimensional case presented in this paper provides a solution of a rather old problem concerning
Noetherianity and Combination Problems
"... Abstract. In abstract algebra, a structure is said to be Noetherian if it does not admit infinite strictly ascending chains of congruences. In this paper, we adapt this notion to firstorder logic by defining the class of Noetherian theories. Examples of theories in this class are Linear Arithmetics ..."
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Abstract. In abstract algebra, a structure is said to be Noetherian if it does not admit infinite strictly ascending chains of congruences. In this paper, we adapt this notion to firstorder logic by defining the class of Noetherian theories. Examples of theories in this class are Linear
NOETHERIANITY OF THE SPACE OF IRREDUCIBLE REPRESENTATIONS
, 2001
"... Abstract. Let R be an associative ring with identity. We study an elementary generalization of the classical Zariski topology, applied to the set of isomorphism classes of simple left Rmodules (or, more generally, simple objects in a complete abelian category). Under this topology the points are cl ..."
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are closed, and when R is left noetherian the corresponding topological space is noetherian. If R is commutative (or PI, or FBN) the topology is equivalent to the Zariski topology, and when R is the first Weyl algebra (in characteristic zero) we obtain a onedimensional irreducible noetherian topological
The length of Noetherian polynomial rings
 Comm. Algebra
"... Abstract. We show that if R is a left Noetherian ring, then lenR[x] = ω ⊗ lenR. Here, for a Noetherian left module A, lenA is its ordinal valued length as defined by Gulliksen [1], and ⊗ is the natural product on ordinal numbers. 1. ..."
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Abstract. We show that if R is a left Noetherian ring, then lenR[x] = ω ⊗ lenR. Here, for a Noetherian left module A, lenA is its ordinal valued length as defined by Gulliksen [1], and ⊗ is the natural product on ordinal numbers. 1.
MULTIPLICITIES OF NOETHERIAN DEFORMATIONS
"... Abstract. The Noetherian class is a wide class of functions defined in terms of polynomial partial differential equations. It includes functions appearing naturally in various branches of mathematics (exponential, elliptic, modular, etc.). A conjecture by Khovanskii states that the local geometry o ..."
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Abstract. The Noetherian class is a wide class of functions defined in terms of polynomial partial differential equations. It includes functions appearing naturally in various branches of mathematics (exponential, elliptic, modular, etc.). A conjecture by Khovanskii states that the local geometry
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