An Extension of the Fugledge Commutativity Theorem Modulo the Hilbert- Schmidt Class to Operators of the Form ΣM n XN n

1983 ◽  
Vol 278 (1) ◽  
pp. 1 ◽  
Author(s):  
Gary Weiss
Keyword(s):  
Commutativity Theorem

scholarly journals A commutativity theorem for lefts-unital rings

1990 ◽  
Vol 13 (4) ◽  
pp. 769-774
Author(s):  
Hamza A. S. Abujabal
Keyword(s):  
Commutativity Theorem ◽  
Unital Ring ◽  
Commutativity Theorems ◽  
Associative Rings ◽  
Unital Rings

In this paper we generalize some well-known commutativity theorems for associative rings as follows: LetRbe a lefts-unital ring. If there exist nonnegative integersm>1,k≥0, andn≥0such that for anyx,yinR,[xky−xnym,x]=0, thenRis commutative.

scholarly journals A Commutativity theorem for semiprime rings

1980 ◽  
Vol 30 (1) ◽  
pp. 33-36
Author(s):  
Vishnu Gupta
Keyword(s):  
Positive Integer ◽  
Semiprime Ring ◽  
Commutativity Theorem ◽  
Semiprime Rings

AbstractIt is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.

scholarly journals A generalized commutativity theorem for pk-quasihyponormal operators

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 77-83
Author(s):  
B.P. Duggal
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Commutativity Theorem ◽  
Hilbert Space Operators

For Hilbert space operators A and B, let ?AB denote the generalized derivation ?AB(X) = AX - XB and let /\AB denote the elementary operator rAB(X) = AXB-X. If A is a pk-quasihyponormal operator, A ? pk - QH, and B*is an either p-hyponormal or injective dominant or injective pk - QH operator (resp., B*is an either p-hyponormal or dominant or pk - QH operator), then ?AB(X) = 0 =? SA*B*(X) = 0 (resp., rAB(X) = 0 =? rA*B*(X) = 0). .

A Commutativity Theorem for Rings with Involution

1978 ◽  
Vol 30 (6) ◽  
pp. 1121-1143
Author(s):  
M. Chacron
Keyword(s):  
Prime Ring ◽  
Associative Ring ◽  
Commutativity Theorem ◽  
Period 2 ◽  
Rings With Involution ◽  
Symmetric Element

A ring with involution R is an associative ring endowed with an antiautomorphism * of period 2. One of the first commutativity results for rings with * is a theorem of S. Montgomery asserting that if R is a prime ring, in which every symmetric element s = s* is of the form s — sn(s) (n(s) ≧ 2), then either R is commutative or R is the 2 X 2 matrices over a field, which is a nice generalization of a well-known theorem of N. Jacobson on rings all of whose elements x = xn(x).

A commutativity theorem for hermitian operators

1976 ◽  
Vol 220 (3) ◽  
pp. 215-217 ◽  
Author(s):  
H. R. Dowson ◽  
T. A. Gillespie ◽  
P. G. Spain
Keyword(s):  
Commutativity Theorem
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