EXTERNAL APPROACH OF IDEALS IN SUBTRACTION ALGEBRAS

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Kellil*, R. (2013). EXTERNAL APPROACH OF IDEALS IN SUBTRACTION ALGEBRAS. Asian Journal of Current Engineering and Maths, 2(2). Retrieved from http://innovativejournal.in/index.php/ajcem/article/view/158
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Abstract

In this paper we are inspired by the work of Young Bae Jun and Kyung  Ho Kim. We introduce another definition of the notion of ideal of a subtraction  algebra, which infers then a different notion of prime ideal.  This notion leaves the principle that if an ideal contains an element it  contains all the elements which are lower than it, while that proposed  in  the paper quoted previously if an element y is in the ideal and if the element  x – y  is in the ideal then x is also in the ideal. Certain results steel valid in our case. We think that the definitions which we introduced are less restrictive than those of Young Bae Jun and Kyung Ho Kim. We introduce besides the notion of morphism of a subtraction algebra and establish some relative characterizations of the kernels of such morphisms.

1991 Mathematics Subject Classification. 06A99, 06A06, 03E20,03E15.

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