The structure of pan-addition operator with pre-determined pan-multiplication

Authors:
Xiaojun Tong;Mianyun Chen;Yi Lin
Affiliations:
Department of Mathematics and Physics, Wuhan Polytechnic University, Wuhan 430023, PR China;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China;Department of Mathematics, Slippery Rock University, Slippery Rock, PA 16057, USA
Venue:
Information Sciences: an International Journal
Year:
2006

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Abstract

Based on the structure of general pan-multiplication operators and the theory of first order linear partial differential equations, we study the structure of pan-addition operators with pre-determined pan-multiplication operators. At first, we describe the structure of pan-addition operators under the ordinary multiplication. Then, with this structure in place, we derive the general representation for the structure of pan-addition operators.