Elementary Divisor Domains as Endomorphism Rings

2020 ◽  
pp. 33-40
Author(s):  
László Fuchs
Keyword(s):  
Elementary Divisor ◽  
Endomorphism Rings

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

Some Criteria for Hermite Rings and Elementary Divisor Rings

1974 ◽  
Vol 26 (6) ◽  
pp. 1380-1383 ◽  
Author(s):  
Thomas S. Shores ◽  
Roger Wiegand
Keyword(s):  
Triangular Matrix ◽  
Elementary Divisor ◽  
Diagonal Matrix ◽  
Finitely Generated ◽  
Elementary Divisor Ring ◽  
Hermite Ring

Recall that a ring R (all rings considered are commutative with unit) is an elementary divisor ring (respectively, a Hermite ring) provided every matrix over R is equivalent to a diagonal matrix (respectively, a triangular matrix). Thus, every elementary divisor ring is Hermite, and it is easily seen that a Hermite ring is Bezout, that is, finitely generated ideals are principal. Examples have been given [4] to show that neither implication is reversible.

Noncommutative elementary divisor rings

1988 ◽  
Vol 39 (4) ◽  
pp. 349-353
Author(s):  
B. V. Zabavskii
Keyword(s):  
Elementary Divisor

Anti-isomorphisms of the endomorphism rings of a class of free modules

1965 ◽  
Vol 159 (4) ◽  
pp. 278-284 ◽  
Author(s):  
Leonard Gewirtzman
Keyword(s):  
Endomorphism Rings ◽  
Free Modules

Isomorphisms and anti-isomorphisms of endomorphism rings of graded modules close to free ones

2009 ◽  
Vol 79 (2) ◽  
pp. 255-257 ◽  
Author(s):  
I. N. Balaba ◽  
A. V. Mikhalev
Keyword(s):  
Endomorphism Rings ◽  
Graded Modules

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.

Self-Small Abelian Groups as Modules over Their Endomorphism Rings

2003 ◽  
Vol 31 (10) ◽  
pp. 4911-4924 ◽  
Author(s):  
Simion Breaz
Keyword(s):  
Abelian Groups ◽  
Endomorphism Rings

scholarly journals Some modules with nearly prescribed endomorphism rings

1972 ◽  
Vol 23 (2) ◽  
pp. 250-262 ◽  
Author(s):  
Sheila Brenner
Keyword(s):  
Endomorphism Rings
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