Geodesic
Associative algebras satisfying asemigroup identity
Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 453-462

Voir la notice de l'article provenant de la source Cambridge University Press

Denoteby $(R,\cdot)$ the multiplicative semigroup of an associative algebra$R$ over an infinite field, and let $(R,\circ)$ represent $R$ whenviewed as a semigroup via the circle operation $x\circy=x+y+xy$. In thispaper we characterize the existence of an identity in these semigroupsin terms of the Lie structure of $R$. Namely, we prove that thefollowing conditions on $R$ are equivalent: the semigroup $(R,\circ)$satisfies an identity; the semigroup $(R,\cdot)$ satisfies a reducedidentity; and, the associated Lie algebra of $R$ satisfies the Engelcondition. When $R$ is finitely generated these conditions are eachequivalent to $R$ being upper Lienilpotent.1991 Mathematics Subject Classification 16R40, 20M07, 20M25 
Riley, David M.; Wilson, Mark C. Associative algebras satisfying asemigroup identity. Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 453-462. doi: 10.1017/S0017089599000142
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     title = {Associative algebras satisfying asemigroup identity},
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     year = {1999},
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     number = {3},
     doi = {10.1017/S0017089599000142},
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