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Polynomial near-rings in k indeterminates

Published online by Cambridge University Press:  17 April 2009

Enoch K.S. Lee  and
Nico J. Groenewald
Enoch K.S. Lee
Affiliation:
Mathematics Department, Ferris State University, Big Rapids, MI 49307, United States of America, e-mail: leee@ferris.edu
Nico J. Groenewald
Affiliation:
Mathematics Department, University of Port Elizabeth, P.O. Box 1600, Port Elizabeth, South Africa, e-mail: nico.groenewald@upe.ac.za
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Polynomial near-rings in k-commuting indeterminates are our object of study. We illustrate out work for k = 2, that is, N[x, y] as an extension to N[x], while the case for arbitrarily k follows easily. Our approach is different from the recursive definition N[x][y]. However, it can be shown that N[x, y] is isomorphic to N[x][y]. Several important tools such as the degree, the least degree, et cetera are defined with respect to N[x, y]. We also clarify some notations involved in defining polynomial near-rings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 441 - 449
Copyright
Copyright © Australian Mathematical Society 2004

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