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On rings which are
sums of two PI-subrings: a combinatorial approach
B. Felzenszwalb, A. Giambruno and G. Leal |
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Vol. 209 (2003), No. 1, 17–31
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Abstract |
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We study the following open question: If a ring R is the sum of two subrings A and B both satisfying a polynomial identity, does R itself satisfy a polynomial identity? We give a positive answer to this question in case R satisfies a special “mixed” identity or (AB)k ⊆ A for some k ≥ 1 or A or B is a Lie ideal. Our approach is based on a comparative analysis of the sequences of codimensions of the three rings and their asymptotics. As a reward we obtain a bound on the degree of a polynomial identity satisfied by R as a function of the degree of an identity satisfied by A and B. |
Milestones
Received: 15 October 2001
Revised: 16 April 2002
Published: 1 March 2003
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Authors |
| B. Felzenszwalb | |
| Instituto de Matemática Universidade Federal do Rio de Janeiro Rio de Janeiro Brazil |
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| A. Giambruno | |
| Dipartimento di Matematica ed
Applicazioni Università di Palermo Via Archirafi 34 90123 Palermo Italy |
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| G. Leal | |
| Instituto de Matemática Universidade Federal do Rio de Janeiro Rio de Janeiro Brazil |
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