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Polynomial Identity Rings
Paperback
Series: Advanced Courses in Mathematics - Crm Barcelona
AlgebraGeneral ComputersGeneral Mathematics
ISBN13: 9783764371265
Publisher: Birkhauser
Published: May 25 2004
Pages: 200
Weight: 0.83
Height: 0.45 Width: 7.00 Depth: 10.00
Language: English
A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x, y) = xy - yx and exterior algebras satisfy the polynomial f(x, y, z) = (xy - yx)z - z(xy - yx). Satisfying a polynomial identity is often regarded as a generalization of commutativity. These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity.
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