Relationships between the canonical ascending and descending central series of ideals of an associative algebra |
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| Authors: | David Riley Mayada Shahada |
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| Institution: | 1. Department of Mathematics, Western University, London, Ontario, Canadadmriley@uwo.ca;3. Department of Mathematics, Western University, London, Ontario, Canada |
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| Abstract: | We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results. |
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| Keywords: | Central series Lie nilpotence strong Lie nilpotence upper Lie nilpotence verbal and marginal subspaces |
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