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Abstract and Applied Analysis
Volume 2014, Article ID 654798, 8 pages
Research Article

Regularity of Functions on the Reduced Quaternion Field in Clifford Analysis

Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea

Received 11 December 2013; Revised 12 February 2014; Accepted 18 February 2014; Published 20 March 2014

Academic Editor: Junesang Choi

Copyright © 2014 Ji Eun Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define a new hypercomplex structure of and a regular function with values in that structure. From the properties of regular functions, we research the exponential function on the reduced quaternion field and represent the corresponding Cauchy-Riemann equations in hypercomplex structures of .