commutativity theorems for rings and groups with constraints on commutators
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ID: 182444
1984
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Abstract
Let n>1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn,y]=[x,ym]ys for all x, y in R. If, further, R is n-torsion free, then R is commutativite. If n-torsion freeness of R is replaced by m, n are relatively prime, then R is still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t=s=0 and m=n+1.
| Reference Key |
psomopoulos1984internationalcommutativity
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|---|---|
| Authors | ;Evagelos Psomopoulos |
| Journal | structural engineering and mechanics |
| Year | 1984 |
| DOI |
10.1155/S0161171284000569
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