Endomorphism rings of essential extensions of a noetherian module

1974 ◽  
Vol 17 (1) ◽  
pp. 46-49 ◽  
Author(s):  
M. G. Deshpande ◽  
E. H. Feller
Keyword(s):  
Endomorphism Rings ◽  
Noetherian Module ◽  
Essential Extensions

Structure of Some Noetherian Injective Modules

1980 ◽  
Vol 32 (6) ◽  
pp. 1277-1287 ◽  
Author(s):  
B. Sarath
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Finitely Generated ◽  
Endomorphism Rings ◽  
Commutative Case ◽  
Noetherian Module ◽  
Direct Sum ◽  
Injective Modules ◽  
Semiprime Rings ◽  
Noetherian Modules

The main object of this paper is to study when infective noetherian modules are artinian. This question was first raised by J. Fisher and an example of an injective noetherian module which is not artinian is given in [9]. However, it is shown in [4] that over commutative rings, and over hereditary noetherian P.I rings, injective noetherian does imply artinian. By combining results of [6] and [4] it can be shown that the above implication is true over any noetherian P.I ring. It is shown in this paper that injective noetherian modules are artinian over rings finitely generated as modules over their centers, and over semiprime rings of Krull dimension 1. It is also shown that every injective noetherian module over a P.I ring contains a simple submodule. Since any noetherian injective module is a finite direct sum of indecomposable injectives it suffices to study when such injectives are artinian. IfQis an injective indecomposable noetherian module, thenQcontains a non-zero submoduleQ0such that the endomorphism rings ofQ0and all its submodules are skewfields. Over a commutative ring, such aQ0is simple. In the non-commutative case very little can be concluded, and many of the difficulties seem to arise here.

scholarly journals Endomorphism Rings Via Minimal Morphisms

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Manuel Cortés-Izurdiaga ◽  
Pedro A. Guil Asensio ◽  
D. Keskin Tütüncü ◽  
Ashish K. Srivastava
Keyword(s):  
Endomorphism Rings

On the computation of the endomorphism rings of abelian surfaces

2021 ◽  
Author(s):  
Claus Fieker ◽  
Tommy Hofmann ◽  
Sogo Pierre Sanon
Keyword(s):  
Abelian Surfaces ◽  
Endomorphism Rings

scholarly journals Quotient rings of Noetherian module finite rings

1994 ◽  
Vol 121 (2) ◽  
pp. 335-335 ◽  
Author(s):  
A. W. Chatters ◽  
C. R. Hajarnavis
Keyword(s):  
Finite Rings ◽  
Noetherian Module ◽  
Quotient Rings

Multiplication complexe et équivalence élémentaire dans le langage des corps (Complex multiplication and elementary equivalence in the language of fields)

2002 ◽  
Vol 67 (2) ◽  
pp. 635-648
Author(s):  
Xavier Vidaux
Keyword(s):  
Function Fields ◽  
Complex Multiplication ◽  
Closed Field ◽  
Constant Symbol ◽  
Endomorphism Rings ◽  
Modular Invariant ◽  
Elementary Equivalence ◽  
Algebraically Closed Field

AbstractLet K and K′ be two elliptic fields with complex multiplication over an algebraically closed field k of characteristic 0. non k-isomorphic, and let C and C′ be two curves with respectively K and K′ as function fields. We prove that if the endomorphism rings of the curves are not isomorphic then K and K′ are not elementarily equivalent in the language of fields expanded with a constant symbol (the modular invariant). This theorem is an analogue of a theorem from David A. Pierce in the language of k-algebras.

scholarly journals On essential extensions of rings

1987 ◽  
Vol 35 (3) ◽  
pp. 379-386 ◽  
Author(s):  
E. R. Puczyłwski
Keyword(s):  
Ring Theory ◽  
Essential Ideal ◽  
Essential Extensions

This paper concerns the problem of description of the set of rings containing a given ring as an essential ideal. The results obtained are applied to some problems of ring theory and radicals.

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