A commutativity theorem for division rings and an extension of a result of Faith

1996 ◽  
Vol 30 (3-4) ◽  
pp. 302-309
Author(s):  
Jairo Z. Gonçalves ◽  
Arnaldo Mandel
Keyword(s):  
Commutativity Theorem ◽  
Division Rings

scholarly journals A commutativity theorem for division rings

1980 ◽  
Vol 21 (1) ◽  
pp. 43-46 ◽  
Author(s):  
Hazar Abu-Khuzam ◽  
Adil Yaqub
Keyword(s):  
Positive Integer ◽  
Division Ring ◽  
Commutativity Theorem ◽  
Division Rings

The following theorem is proved: Let D be a division ring such that for all x, y in D there exists a positive integer n = n(x, y) for which (xy)n − (yx)n is in the center of D. Then D is commutative. This theorem also holds for semisimple rings.

scholarly journals A Commutativity Theorem for Division Rings

1980 ◽  
Vol 23 (2) ◽  
pp. 241-243 ◽  
Author(s):  
Anthony Richoux
Keyword(s):  
Division Ring ◽  
Monic Polynomial ◽  
Commutativity Theorem ◽  
Division Rings ◽  
Integer Coefficients

AbstractLet D be a division ring with center Z. Suppose for all xϵD, there exists a monic polynomial, fx(t), with integer coefficients such that fx(x)ϵZ. Then D is commutative.

On division rings generated by polycyclic groups

1984 ◽  
Vol 47 (2-3) ◽  
pp. 154-164 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Division Rings ◽  
Polycyclic Groups

Polynomials over division rings

1978 ◽  
Vol 31 (3-4) ◽  
pp. 353-358 ◽  
Author(s):  
S. A. Amitsur ◽  
Lance W. Small
Keyword(s):  
Division Rings

scholarly journals Subgroups of finite index in an additive group of a ring

2001 ◽  
Vol 27 (2) ◽  
pp. 83-89
Author(s):  
Doostali Mojdeh ◽  
S. Hassan Hashemi
Keyword(s):  
Finite Index ◽  
Additive Group ◽  
Infinite Field ◽  
Division Rings ◽  
Invertible Elements

IfKis an infinite field andG⫅Kis a subgroup of finite index in an additive group, thenK∗=G∗G∗−1whereG∗denotes the set of all invertible elements inGandG∗−1denotes all inverses of elements ofG∗. Similar results hold for various fields, division rings and rings.

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