Summability of a ring of endomorphisms of vector groups

1998 ◽  
Vol 37 (1) ◽  
pp. 48-55
Author(s):  
A. M. Sebel’din
Keyword(s):  
Ring Of Endomorphisms

Permutation endomorphisms and refinement of a theorem of Birkhoff

1960 ◽  
Vol 56 (4) ◽  
pp. 322-328 ◽  
Author(s):  
H. K. Farahat ◽  
L. Mirsky
Keyword(s):  
Abelian Group ◽  
Finite Number ◽  
Linear Combination ◽  
Finite Linear Combination ◽  
Usual Manner ◽  
Restricted Permutation ◽  
Image Position ◽  
Ring Of Endomorphisms ◽  
Finite Linear

Let be a free additive abelian group, and let be a basis of , so that every element of can be expressed in a unique way as a (finite) linear combination with integral coefficients of elements of . We shall be concerned with the ring of endomorphisms of , the sum and product of the endomorphisms φ, χ being defined, in the usual manner, by the equationsA permutation of a set will be called restricted if it moves only a finite number of elements. We call an endomorphism of a permutation endomorphism if it induces a restricted permutation of the basis .

scholarly journals Bounded topologies on endomorphism rings

2011 ◽  
Vol 20 (1) ◽  
pp. 1-3
Author(s):  
HOREA F. ABRUDAN ◽  
Keyword(s):  
Abelian Group ◽  
Endomorphism Rings ◽  
Ring Topology ◽  
Left And Right ◽  
Ring Of Endomorphisms

We prove in this note that the ring of endomorphisms of an infinite bounded Abelian group admits a nondiscrete right bounded ring topology. We give an example of an Abelian group whose ring of endomorphisms admits both nondiscrete left and right bounded topologies but does not admit a nondiscrete bounded ring topology.

scholarly journals Full subrings of E-rings

1996 ◽  
Vol 54 (2) ◽  
pp. 275-280
Author(s):  
Shalom Feigelstock
Keyword(s):  
Additive Group ◽  
Left Multiplication ◽  
Ring Of Endomorphisms ◽  
Torsion Free

A ring R is said to be an E-ring if the map R → of E (R)+ into the ring of endomorphisms of its additive group via a ↪ al = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group Rl, of left multiplication maps by elements of R, is a full subgroup of E(R)+ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of E-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R+) is an E-ring, and E(R+)+ / is bounded. Some results concerning additive groups of TE-rings will be obtained.

scholarly journals Cycles and Endomorphisms of Abelian Varieties

1954 ◽  
Vol 7 ◽  
pp. 95-102 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Abelian Varieties ◽  
Jacobian Variety ◽  
Symmetric Element ◽  
Ring Of Endomorphisms

In the present paper we shall remark that to each class of algebraically equivalent cycles on a Jacobian variety we can attach a symmetric element of the ring of endomorphisms of the variety and shall prove some formulae concerning attached symmetric elements.

Ring of endomorphisms of a free module

1966 ◽  
Vol 7 (5) ◽  
pp. 923-927 ◽  
Author(s):  
G. M. Tsukerman
Keyword(s):  
Free Module ◽  
Ring Of Endomorphisms
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