Polynomial near-rings in k indeterminates

Publisher： Cambridge University Press

E-ISSN： 1755-1633|70|3|441-449

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.70, Iss.3, 2004-12, pp. : 441-449

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

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.

Related content

Near-rings that reduce to rings

By  

Bulletin of the Australian Mathematical Society, Vol. 17, Iss. 1, 1977-08 ,pp. : 135-137 (3)

Cambridge University Press

Access to resources Recommend Favorite

Near-Rings and Partitioned Groups

By Meldrum J. D. P.  

Communications in Algebra, Vol. 35, Iss. 11, 2007-11 ,pp. : 3473-3494 (22)

Taylor & Francis Ltd

Access to resources Recommend Favorite

On loop near-rings

By  

Bulletin of the Australian Mathematical Society, Vol. 19, Iss. 3, 1978-12 ,pp. : 417-435 (19)

Cambridge University Press

Access to resources Recommend Favorite

On the commutativity of near-rings III

By  

Bulletin of the Australian Mathematical Society, Vol. 6, Iss. 3, 1972-06 ,pp. : 459-464 (6)

Cambridge University Press

Access to resources Recommend Favorite

Pseudo-distributive near-rings

By  

Bulletin of the Australian Mathematical Society, Vol. 12, Iss. 3, 1975-06 ,pp. : 449-456 (8)

Cambridge University Press

Access to resources Recommend Favorite