Note Oncertain Field of Fractions
rhotrix, dimension, construction, generalization
Abstract
The set of some real rhotrices of the same dimension D ∗ was defined in [2] to be an integral domain. An example of a finite field M [R3] was given in [4] based on this definition also and on the construction of finite fields presented in [3]. It was discovered that the finite sub collection of the elements of M [R3] as contained in D∗ is not closed under rhotrix addition and hence not an integral domain. More generally, D∗ is not an integral domain as it is not closed under rhotrix addition. This problem affects the field of fractions constructed in [8]. A solution to this problem is provided in this article and the construction method of such fields is reviewed. This reviewed version gives the generalization of such construction as the n-dimensional rhotrices are used.
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References
S Usaini, S Tudunkaya (2011) Note on rhotrices and the construction of finite fields. 30(1), 53-58.
Kailash Patil (2007) Characterization of ideals of rhotrices over a ring and its applications. 27(1), 138-147.
A Ajibade (2003) The concept of rhotrix in mathematical enrichment. 34(2), 175-179.
E Absalom (2011) The concept of Heart-Oriented Rhotrix Multiplication. 11(2), 34-46.
S Usaini, S Tudunkaya (2011) Certain field of fractions. 11(7), 5-8.
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2012-10-09
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