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Engel varieties of associative rings and the number of Mersenne primes

โœ Scribed by David M. Riley


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
114 KB
Volume
261
Category
Article
ISSN
0021-8693

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โœฆ Synopsis


An associative ring R can be viewed as a semigroup via a โ€ข b = a + b + ab, and as a Lie ring via [a, b] = abba. It is known that the Lie ring [R] is nilpotent if and only if the adjoint semigroup (R, โ€ข) is nilpotent (in the sense defined by Mal'cev or by Neumann and Taylor). We prove a similar result for associative rings whose Lie rings satisfy an Engel identity. Mersenne primes appear in an unexpected role.


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